Thompson's contract runs until the end of this season and reports from Glasgow suggest the former Bolton and Aston Villa midfielder was planning to terminate his deal with Celtic before the window closes on January 31.
His agent, Tony McGill, insists he had not had any contact with Leeds, but claimed the prospect of a relegation fight would not scare his client away from Elland Road.
McGill said: "Leeds are in a bit of trouble at the moment but that wouldn't bother Alan. He's got no problem with rolling his sleeves up.
"They're a very big club and if Leeds were interested then I'm sure he'd want to listen to what they had to offer.
"But it's obviously up to Alan, and a lot depends on Celtic as well. We'd need permission from them to start talking to other clubs, and I haven't had any discussions with Leeds.
"If we can't agree something with Celtic then he's more than happy to stay and fight for his place."