Crystal Palace had seemingly been on the verge of signing the 29-year-old until Eagles manager Ian Holloway announced on Thursday morning that Bent had chosen Craven Cottage over Selhurst Park.
Fulham boss Martin Jol was reticent to comment in detail during his briefing on Thursday afternoon, but Lambert confirmed a deal - with the intention of it becoming permanent next summer - is close.
"He's just away down to Fulham," said the Villa boss.
"I think it's well-documented now that he's down there having a medical and that's the last I've heard."
Jol issued a cautious response to the reports.
"I don't know what's happening. Darren's probably doing his own thing. We're not sure about it," he said.
"We don't speculate on players and can only give an answer when a deal is finalised. We'll see in the next day or two.
"We need quality up front and we're trying to get someone in that position in the next week. We need some pace up front.”
Bent swapped Sunderland for Villa for £24 million in 2011, but fell out of favour with