The report quotes Swansea first-team coach Alan Curtis, suggesting a deal is imminent between the two teams:
"(He is) not really interested in signing a new contract and I think Man City have made a bid," said Curtis.
"So it's just a matter of time now before it happens and it's good for both parties.
Sinclair is a surprise capture for City. Given their spending power, many would assume the reigning EPL champions would focus their resources on acquiring marquee names.
Sinclair is a promising young talent, but doesn't belong in that bracket just yet. At 23, his best years are ahead of him and City boss Roberto Mancini must be impressed with how he has fared against top-flight opposition since Swansea earned promotion in 2011.
As a fleet-footed wide forward, Sinclair would add some true, direct pace to the City front line. Although players like Sergio Aguero and Carlos Tevez possess deceptive quickness, particularly in small spaces, neither offers legitimate speed.
That's a quality Sinclair boasts in abundance, and he also offers more of a goal threat than the likes of Adam Johnson and James Milner. Sinclair netted eight times last season, and has the technique and attacking instincts to drift in off the wing and provide a threat through the middle.
Hot on the heels of the capture of young English starlet Jack Rodwell, Sinclair's signing would represent a slight shift in City's transfer approach. A deal for the Swansea youngster would show the Citizens are serious about committing to young talent and potential.
Signing players who can be developed into established stars instead of buying ready-made, high-profile names, is a smart move from Mancini. City's wage bill is bloated with players whose reputations guaranteed big contracts, but whose performances have failed to match those investments.
Sinclair and Rodwell would represent the first positive steps towards more prudent transfer dealings and the construction of a young base, capable of challenging for the EPL for years to come.