He made 16 league starts for us last season and 9 the season before, so it's hardly like staying here is to guaranteed to do wonders for his career. Playing a few less for Chelsea/City and being in the CL and being on more money, why not? It doesn't look to me like he'd be doing any worse for himself at another club.
He got a right wing back spot during a Bellerin spell of awful form / injury. He got some games on the wing when we should have bought an improvement on Walcott and didn't and he got games at CM because we should've bought a replacement for Cazorla and didn't.
If I was him I'd be definitely looking for something new this summer. Either a step up to a better team's bench or a sensible move somewhere like Everton where he'll get a decent wage and play and probably be appreciated.