Sinclair is unwilling to sign a new contract at the Liberty Stadium and there is interest from the Premier League champions.
The 23-year-old winger scored 27 times for the Swans in the 2010/11 season before adding a further eight goals last season as they finished mid-table on their top-flight return.
And like Joe Allen, who left for Liverpool in a £15million deal earlier this month, the former Chelsea man will leave the Welsh club with Swansea's best wishes.
"(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. He's been terrific for us, to be fair, we've had two seasons out of him and he was superb in the Championship and virtually his goals got us promotion.
"And last year as well he wasn't maybe quite as effective as he was his first year - obviously it was a lot tougher opposition - but he's been absolutely magnificent.
"Like Joe 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."
Swansea boss Michael Laudrup is looking to reinvest the funds from the Allen sale to bring in Celtic midfielder Ki Sung-Yueng, after the Scottish club accepted a bid of around £6m for the 23-year-old.