The Cottagers are eager to bring in reinforcements on deadline day, with a deal for AC Milan's Urby Emanuelson believed to be on the cards.
It is possible that Huddlestone could also be on his way in, with a short trip from White Hart Lane to Craven Cottage still in the pipeline.
No agreement has been put in place as yet, though, and Spurs boss Andre Villas-Boas admits he is unsure as to whether a transfer will be pushed through.
He said: "There was an interest from Fulham. I'm not sure if they're going to follow on that interest.
"We've allowed the club to speak to the player. He's a player we rate very highly."
Villas-Boas revealed after Wednesday's 1-1 draw with Norwich that he does not expect there to be too much activity at White Hart Lane on Thursday, but he is keeping all of his options open.
He said: "It's not impossible that a couple of things happen. It's highly unlikely.
"We need to add quality to the squad and our quality to the squad is keeping the players we have now and Lewis (Holtby) arriving."