The 23-year-old is out of contract next summer with Laudrup and Swans chairman Huw Jenkins hoping they could convince him to stay at the Liberty Stadium with improved terms
But the winger, who represented Team GB at the Olympics, appears to have had his head turned by speculation linking him with a shock move to Premier League champions City.
The signing of Jack Rodwell from Everton last week is set to kick off a recruitment drive that will see Roberto Mancini target several of England’s top young talents with Sinclair at the top of the list.
His departure from South Wales now looks inevitable after Laudrup revealed the former Chelsea player does not want to discuss terms over a new deal.
“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 affect him for Saturday.”
Sinclair scored eight goals for Swansea last season as they finished eight in the table and badgered 27 the year before to secure promotion from the Championship.
However he could be swiftly replaced by Valencia’s Pablo Hernandez with Laudrup reportedly keen to sign the 27-year-old after previously working with him in Spain.
Laudrup said: “I had Pablo in Getafe and we had a fantastic year together. He then signed a five-year contract with Valencia.
“He’s done well, Valencia are the third biggest team in Spain. He is a player that I know very well, and he knows me.”