I'm currently a postdoc and I'm planning to apply for faculty positions soon. However, I'm pretty sure that my current supervisor wants me to stay on for another year. When applying for a job, I'm usually required to state 3 referees. Am I expected to state my current supervisor as one of the referees? Is it going to weaken my application if he's not among the 3? Due to the mentioned conflict of interest, I would rather state other people I've been working with...
If you need to list references, you will almost certainly be expected to list your current boss—in this case, your advisor—as a potential reference. At the very least, if you do not, there is a non-insignificant chance that at some point in the interview process you'll be asked at will ask why he wasn't listed. You should have as good of an answer as possible ready.
Note that stating "I'm ready to move on, but he wanted me to stay on" may raise flags for a potential employer, as they could wonder whether this reflects a lack of loyalty on your part.