If the desire to play every week (when fit), is his main motivation, then he'll go irrespective.
If he accepts his career is winding down, & wants to remain involved at City then he'll stay if offered a deal.
I don't know if he has future managerial ambitions, or whether his ambitions are outside football. I could imagine Kompany doing an Imran Khan & becoming a big politician but equally, he might be happy coaching our defenders for a while.
He hasn’t retired from the national team so that could mean he sees himself making the Euro 2020 squad. Also iirc he recently said he wants to play a few more years. So I’m leaning towards thinking the club will offer him a one year extension with a wage reduction and he’ll sign for another club on 2 year deal for example.