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, although Press Association Sport understands 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 ex-Chelsea player does not want to discuss terms.
Sinclair's exit now seems inevitable as Swansea will not want to risk losing him for nothing next summer, although Laudrup intends 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."