The 23-year-old winger is out of contract at the end of this season and reports have linked him with a move to Premier League champions Manchester City. It is understood several clubs have declared an interest.
Laudrup and Swansea chairman Huw Jenkins had hoped to convince Sinclair to extend his stay in south Wales, but the Dane revealed the former Chelsea player does not want to discuss terms.
Sinclair's swift exit now seems inevitable as Swansea will not want to risk losing him for nothing next summer, but Laudrup made it clear he will not hesitate to pick him for Saturday's Premier League opener at QPR.
"I have spoken to Scott and he confirmed what he said to the chairman, that he won't sign a new contract," said Laudrup.
"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.
"If it affects 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 City are interested in signing the Team GB Olympic player, but would not say if Swansea have received a formal offer from the cash-rich Etihad Stadium club.
"I don't know how official it is but there is interest," he said.
"Manchester City is the name that is always coming up but again I have not spoken to them.
"I don't know if it's official."
Sinclair scored eight goals last season as Swansea finished 11th in the Premier League; the season before he scored 27 times and netted a hat-trick in the play-off final win over Reading at Wembley.
The loss of the former England Under-21 international would be another blow to Swansea following the sale of midfielder Joe Allen to Liverpool for a fee of £15million last week.
Manchester United and Liverpool are also being linked with moves for Neil Taylor and Ashley Williams respectively.
But Laudrup was at pains to make it clear there will be no mass exodus from the Liberty Stadium before the transfer window shuts at the end of August.
"It will be a problem if we suddenly lose four or five players," he said. "If it's two or one it is okay, but if you are talking about seven into the first 11 you will need time to adjust.
"But the most important thing is always the club. First the manager and especially the chairman and the board have to think about the club.
"I don't think we have to reach that limit."
Laudrup is reportedly interested in bringing Valencia's Spain international Pablo Hernandez to south Wales.
And should Sinclair make his now expected departure, the 27-year-old, who Laudrup has previously worked with, would be an ideal replacement.
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."
While Sinclair is set to leave the Liberty Stadium, Arsenal's Kyle Bartley has completed a move to South Wales.
The 21-year-old centre-half's move to south Wales is believed to be for a fee of £1million.
He posted on his Twitter account: "Swansea deal complete. Very happy. Was an extremely tough decision for me to leave Arsenal, but felt time was right.
"Swansea offered me an opportunity. And I'm extremely excited to start my career here, will always be thankful to Arsenal for my education."
He added "Was the toughest decision of my life. But it is a permanent deal. And now I'm raring to go with Swansea."