Fulham's official website said manager and former Tottenham boss Martin Jol had confirmed a deal after his side lost 1-0 to Sheffield Wednesday in the League Cup.
"The player is currently undergoing a medical," it said.
Dembele, 25, is regarded as a near like-for-like replacement for Modric, who completed his transfer from North London to Real Madrid on Monday.
Fulham's West London neighbours Queens Park Rangers have also been active as the close of the transfer window approaches, with Inter Milan goalkeeper Julio Cesar on the verge of being snapped up.
Cesar was filmed by British press arriving at Loftus Road ahead of QPR's League Cup match with Walsall and manager Mark Hughes confirmed to reporters after the 3-0 win that he was hopeful of wrapping up a deal for the Brazilian.
Banned QPR midfielder Joey Barton's proposed move to French club Marseille also looks to be in its final stages with his agent Willie Mackay confirming final negotiations were underway.
Barton, who was suspended by the English FA for 12 Premier League matches following his sending off in the final game of last season against Manchester City, looks set to leave as part of a deal to bring defender Stephane Mbia the other way.
"I think you will find that maybe a deal will happen tomorrow with Joey flying out to Marseille and Stephane Mbia will arrive at QPR," Mackay told BBC's Radio 5 live.
