Permitting Question

I am getting ready to sell a home in Arizona, but was considering adding an additional bedroom prior to listing. I have been getting mixed feedback as to whether the project would require permitting from the city. If anyone is able to provide their understanding on this I would greatly appreciate it. Here are some details:

• Not adding any additional square footage. The room would be added within the homes current living room as the room is >50 feet long
• We would not be touching any exterior wall as there is already a window and French door to the backyard
• We would have to reroute the a/c to reach the room
• The only electrical required would be moving the ceiling fan over around 5 feet
• We would not be touching any load bearing walls, just adding two walls and a door to close off the room

My understanding is that we probably do need a permit technically, but every contractor we have spoken to acts like we are insane to waste the time and money. Not sure what the repercussions are of not getting a permit if we have a licensed general contractor complete the work. Any insight would be helpful, thanks!