I can see why he wants a move.
If we strengthen with even one player in midfield and Yaya stays, as is looking the case, Jimmy won't play until we need to sure a game up, or through injuries. I wouldn't want to play that role either at 29 years old, he's probably got 3 seasons playing at a top level, then his decline.
If he can't get a move, on similar money and a hefty signing on fee, to a club like Liverpool he should take it. He'll be a hero for them, he won't win much, possibly a cup, and he'll play every week. He doesn't need to uproot his family and it satisfies his desire to move.
Selfishly I'd love him to stay, I like Milner, I rate him, but if we do strengthen with an international class young midfielder, he just won't get the game time.
Good luck Jimmy, wherever you go, you've been terrific for City since day one.