Which are correct:
1) Here is a list of the reasons why he might have quit his job.
2) Here is a list of the possible reasons why he might have quit his job.
3) Here is a list of the possible reasons why he quit his job.
I think '1' and '2' are ambiguous.
They could mean:
a) He might have quit his job. Here is a list of the reasons why I am saying he might have quit his job.
and they could also mean '3' (He has quit his job. Here is a list of the possible reasons.)
Would you say that is correct?.
Although this is not your point, "reason" and "why" are rarely needed in the same sentence.
This is the reason he did this.
This is why he did this.
This is a list of reasons that he may have...
I certainly did not think it was reasons you think he may have quit. I thought (only) that it was reasons that led him to quit.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.