Jol worked with the midfielder in his stint at White Hart Lane but, with injury troubles continuing to curtail his form, Huddlestone has slowly moved down the pecking order in North London.
With Fulham still desperate to plug a gaping hole left in midfield by the departures of Moussa Dembele, Dickson Etuhu and Danny Murphy, Jol's admiration for the former England international could signal a resurrected move for the player.
Fulham have tested Spurs' hand before but they have always been reluctant to let him leave, particularly on loan. Jol, however, would prefer a move to be temporary and will attempt to persuade Andre Villas-Boas into agreeing a deal.
Speaking ahead of the game against Wigan Athletic on Saturday, Jol said:
"Over the last six years I had an interest in Tom Huddlestone, but he was injured and then went to Stoke. I think he failed a medical there but I am not sure, so he went back to Spurs.
"If Tom is fit, he is always in the back of my mind but as I told you before, I won't speculate on names. I can't say Tom is not on my list because I like him."