As revealed by Goal.com, the Premier League champions have made a £6 million bid for the forward but Swans chairman Huw Jenkins criticised them on Tuesday for being sluggish in their pursuit.
And Laudrup told Sky Sports of the deal: "I can't say, I really don't know where we are at the moment.
"Even if talks have broken down there is still time for everything to happen, I am not saying he will go, or he will stay.
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"From a manager's point of view, Scott is an important player and he plays in a position where we don't have that many players and if he leaves we need another one.
"That's the balancing act and the closer we get to the deadline the more difficult and shaky it will be."
Marvin Emnes of Middlesbrough and Pablo Hernandez of Valencia have been touted as potential replacements for Sinclair should he leave and the former Real Mallorca coach is bracing himself for a frantic end to the transfer window.
"I think it will be very busy," the Danish legend continued.
"Everyone here will have to be working hard over the next three days to make sure we are not in a situation where a club is saying 'the fax is not working'.
"I tried that, where a fax wasn't working in a club and they signed a player a little too late.
"Luckily I think we have two or three fax machines here."