The young England international has just 12 months left to run on his current contract at the Liberty Stadium.
However, with the Citizens looking to acquire the 23-year-old, Swans manager Michael Laudrup has confirmed that Sinclair will not be signing an extension with the club.
"I have spoken to Scott and he confirmed what he said to the chairman that he won't sign a new contract," he said. "But he is here now and that's what important for me.
"You never know what will happen tomorrow or the day after but there is no point arguing about it, we have to get on with it. Until August 31 anything can happen.
"Of course there is interest from a big club in Scott but the only thing I care about in the short term is that it does not effect him for Saturday. If it effects the player then we have to talk about.
"I will talk to Scott and if he says no he does not want to play then we will see, if he says 'I'm a professional' then I know he is in the squad."
Laudrup admitted that City are interested in signing Sinclair, but stopped short of saying whether they had received a bid from the Premier League champions.
"I don't know how official it is but there is interest," he added. "Manchester City is the name that is always coming up but again I have not spoken to them.
"But I don't know if it's official."
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