The 23-year-old signed for the Premier League champions during the summer, but has, as of yet, failed to force himself into the starting XI.
This has tempted the Toffees, who feel that they may be able to lure him to Goodison Park for six months with the prospect of regular first-team football.
City are rumoured to be willing to allow their £8m man to leave on a temporary basis to gain experience, however it is thought that Sinclair is keen to fight for his place at the Etihad Stadium.
But, having made only two league starts this term, the former Swansea star may change his mind, especially if the Sky Blues draft in a big money star during January.
QPR are also thought to be interested, but the prospect of fighting for European qualification may be more tempting than a possible relegation dogfight with the London club.
One potential stumbling block could be Sinclair’s wage demands, which Everton boss David Moyes is rumoured to unwilling to match.
If a compromise between the two clubs could be agreed then the Merseyside team would be keen to push through a deal.
Sinclair enjoyed a fine season with Swansea last term, helping the South Wales outfit maintain their top-tier status.