Back in ASOS, Tywin encourages Tyrion to bed Sansa due to the possibility that their marriage could be set aside:

"She is old enough to be Lady of Winterfell once her brother is dead. Claim her maidenhood and you will be one step closer to claiming the north. Get her with child, and the prize is all but won. Do I need to remind you that a marriage that has not been consummated can be set aside?"
"By the High Septon or a Council of Faith. Our present High Septon is a trained seal who barks prettily on command. Moon Boy is more like to annul my marriage than he is." -ASOS, Tyrion IV

I thought it would be interesting to see how this could affect Sansa's plotline going forward.

What to do with Sansa's marriage to Tyrion?

First Lysa/Littlefinger scheme to marry Sansa to Sweetrobin, but are waiting for Tyrion's death:

"I . . . I am married, my lady."
"Yes, but soon a widow. Be glad the Imp preferred his whores. It would not be fitting for my son to take that dwarf's leavings, but as he never touched you . . . How would you like to marry your cousin, the Lord Robert?" -ASOS, Sansa VI

Then Littlefinger plans to marry Sansa to Harry the Heir after Cersei has Tyrion executed, but Tyrion escapes before this can happen:

Petyr Baelish took her by the hand and drew her down onto his lap. "I have made a marriage contract for you."
"A marriage . . ." Her throat tightened. She did not want to wed again, not now, perhaps not ever. "I do not . . . I cannot marry. Father, I . . ." Alayne looked to the door, to make certain it was closed. "I am married," she whispered. "You know."
Petyr put a finger to her lips to silence her. "The dwarf wed Ned Stark's daughter, not mine. Be that as it may. This is only a betrothal. The marriage must needs wait until Cersei is done and Sansa's safely widowed. And you must meet the boy and win his approval. Lady Waynwood will not make him marry against his will, she was quite firm on that." -AFFC, Alayne II

and:

No man can wed me so long as my dwarf husband still lives somewhere in this world. Queen Cersei had collected the head of a dozen dwarfs, Petyr claimed, but none were Tyrion's. "Sweetrobin, you must not say such things. You are the Lord of the Eyrie and Defender of the Vale, and you must wed a highborn lady and father a son to sit in the High Hall of House Arryn after you are gone." -TWOW, Arianne I

With that in mind, in order for Sansa to marry anyone one of the following needs to happen:

• Tyrion dies
• The High Septon annuls the marriage
• A Council of Faith annuls the marriage
• A Ruling Monarch annuls the marriage

Note: I've seen it argued since Sansa did willingly marry Tyrion it doesn't count. I don't believe this is the case as we see numerous marriages throughout history where one or both of the parties aren't necessarily interested. (Ex: Lady Hornwood/Ramsay Snow).

I will tell my aunt that I don't want to marry Robert. Not even the High Septon himself could declare a woman married if she refused to say the vows. -ASOS, Sansa VII

Note II: It is also possible that Sansa and Tyrion remain married

Note III: There are examples of lords annulling marriages before the Faith of the Seven was established.

Note IV: For the most part, followers of the different gods respect the sanctity of marriages made by other religions (likely political).

Since I find it unlikely that Tyrion dies any time soon, I think it would be best to explore the other two options

The High Septon annuls the marriage

The current High Septon/Sparrow is not the lickspittle that some of his predecessors were. The question would be why would this High Septon want to annul Sansa/Tyrion's marriage?

Personally I think Sansa's plotline heads north, but lets say (ashford) that Sansa is a potential marriage option for Young Griff. Even with her being a northerner (out of the Starks I would argue that Sansa is the most focused on the Seven), the High Septon could probably see how this could be advantageous.

If interested: Young Griff and King's Landing

If Young Griff is crowned by the High Septon/Sparrow, then I think the High Sparrow could see the help this wedding could potentially provide.

Again I think Sansa' plotline heads north but here are GRRM's words on Sansa's marriage/the High Septon:

Q: Can a marriage be annulled without both parties present and without sansa revealing who she really is?
GRRM: No one needs to be present to annul a marriage
Q: How?
GRRM: Sansa would need to request it
Q: As Sansa?
GRRM: Well, why would a High Septon consider a request from anyone but the parties involved?
Q: I mean she can't hide who she is. she has to request that her marriage, her being Sansa Stark, to Tyrion Lannister be annulled, which would imply that the High Septon would need to know that Sansa Stark is requesting the annulment of her marriage. Which would reveal, to a certain extent where Sansa is.
GRRM: yes indeed -SSM, Minisa Tully & Sansa: 9 Sept 2000

A Council of Faith annuls the marriage

As far as I know we don't get any examples of "councils of faith" in the series excluding Tyrion's mention.

That said it could be argued that a Council of Faith is what Tywin used to end Tyrion's:

After he was done with her, my father had the marriage undone. It was as if we had never been wed, the septons said." He squeezed her hand. "Please, let's have no more talk of the Tower of the Hand. You will be in the kitchens only a little while. Once we're done with Stannis, you'll have another manse, and silks as soft as your hands." -ACOK, Tyrion V

Monarch annuls the marriage

A monarch can do as he or she pleases (obviously there are always consequences to any action), but we see numerous examples in history of someone urging monarch to set aside their own spouse (even consummated) or a spouse of the royal family:

had likewise proved a barren union, and though Viserys I refused his brother's entreaties to set aside the marriage, he did recall him to court to take up the burden of rule. -TWOIAF, The Targaryen Kings: Viserys I

and:

Aerys was learned, in his way, though his interests were largely to do with dusty tomes concerned with ancient prophecy and the higher mysteries. Wed to Aelinor Penrose, he never showed an interest in getting her with child, and rumor had it that he had even failed to consummate the marriage. His small council, at their wits' ends, hoped it was simply some dislike of her that moved him, and thus they urged him to put her aside to take another wife. But he would not hear of it. -TWOIAF, The Targaryen Kings: Aerys I

and:

It was true that Aegon had been a friend to the smallfolk, had practically grown up among them, but to countenance the marriage of the heir to the throne to a commoner of uncertain birth was beyond him. His Grace did all he could to have the marriage undone, demanding that Duncan put Jenny aside. The prince shared his father's stubbornness, however, and refused him. Even when the High Septon, Grand Maester, and small council joined together to insist King Aegon force his son to choose between the Iron Throne and this wild woman of the woods, Duncan would not budge. Rather than give up Jenny, he foreswore his claim to the crown in favor of his brother Jaehaerys, and abdicated as Prince of Dragonstone. -TWOIAF: The Targaryen Kings: Aegon V

Silent Sisters/Night's Watch/Kingsguard

We also see examples of marriages ending when one or both parties join an order which requires celibacy:

King Aegon promised to raise him to the Kingsguard, so Fireball made his wife join the silent sisters, only by the time a place came open, King Aegon was dead and King Daeron named Ser Willam Wylde instead. -The Mystery Knight

and:

Tyrion stabbed listlessly at a greasy grey sausage, wishing it were his sister. It is bloody cold on the Wall, but at least I would be shut of Cersei. He did not think he would make much of a ranger, but the Night's Watch needed clever men as well as strong ones. Lord Commander Mormont had said as much, when Tyrion had visited Castle Black. There are those inconvenient vows, though. It would mean the end of his marriage and whatever claim he might ever have made for Casterly Rock, but he did not seem destined to enjoy either in any case. And he seemed to recall that there was a brothel in a nearby village. -ASOS, Tyrion X

while keeping in mind there is some potential connections to Tyrion and the Night's Watch from his early visit:

Jaime smiled. "I hope you're not thinking of taking the black on us, sweet brother." - AGOT, Tyrion I

and:

"Past certain, Lord Mormont," Tyrion replied. "My brother Jaime will be wondering what has become of me. He may decide that you have convinced me to take the black." -AGOT, Tyrion III

As I mentioned above there is no guarantee it is ever ended, but I just wanted to list the different ways in which this marriage could be dissolved (obviously it could also be dissolved amicably in the future as well). but in my opinion the likeliest ways for this to happen is the High Septon (especially after what the Lannisters did to the last High Septon). A Council of Faith is possible but I don't know if Littlefinger has the power to do so (even as "Lord of Harrenhal") or else he would have done so already.

That said I think that Sansa's plotline heads north to a potential contentious situation in the north instead of south (for instance the ashford theory).

TLDR: A list of potential ways that Sansa/Tyrion's marriage could be ended.