The former Swansea star has made only a handful of appearances since moving to the club and Aston Villa are among those outfits ready to offer him a temporary stay with them.
Sinclair recently made it clear that he wanted to prove himself with the champions after hearing of Everton's reported interest in him.
Villa boss Paul Lambert believes the winger can boost their survival chances by serving up the chances for his shot-shy strikers and hopes the prospect of regular first team football for the remainder of the season with tempt Sinclair to make the move.
Sinclair is no stranger to loan deals in his career, having previously enjoyed spells at Plymouth Argyle, QPR, Charlton, Crystal Palace, Birmingham and Wigan during his time on Chelsea's books.
City forked out £6.7 million on the player, who scored 35 goals in his two seasons at the club, following Adam Johnson's departure to Sunderland in the summer.
Newcastle are also interested in the 23-year-old, while Everton boss David Moyes is certain to come back in with a fresh offer if he senses that Sinclair's stance on a move has changed.
Man City last week