Background check for new job, should I allow to contact my current employer before I resigned?

I’ve received and signed a contract for a new job starting in January. I’m now completing the pre-employment screening with a third-party provider, and one of the questions asks whether they can contact my current employer for a reference.

The issue is that I haven’t handed in my notice yet. I have a three-month notice period and planning to give my notice at the end of the month.

Should I allow them to contact my current employer now, or select that they can’t contact them? I obviously don’t want my current employer finding out that I’m leaving before I’ve formally resigned. What would happen if I select 'no' to that question?

What’s the best way to handle this during pre-employment screening?