The Team GB midfielder has been linked throughout the summer with a move away from the Liberty Stadium, with the Premier League champions at the head of the queue for Sinclair's signature.
The 23-year-old will not sign a new deal with the Swans, and Curtis says that the sale of Sinclair is likely to happen before the end of the current transfer window.
"He's not really interested in signing a new contract and I think Man City have made a bid," Curtis said.
"So it's just a matter of time now before it happens and it's good for both parties.
"Like Joe [Allen, who joined Liverpool] we wish him all the best, but as long as the club keeps pushing forward that's the main thing. It obviously gives Scott the chance to settle in at his new club and it gives us the opportunity to buy a replacement for Scott."
Sinclair scored eight goals in Swansea's debut Premier League season last year.