The Daily Mail says Fulham are keen to strengthen their midfield and are considering a January move for Trotter.
Chief scout Barry Simmonds has watched the 23-year-old numerous times over the past few weeks as Jol looks to finalise transfer plans.
Trotter has been watched by a clutch of Barclays Premier League clubs this season, including Arsenal, Wolves, Everton and Bolton. But Fulham are understood to be the most interested going into the transfer window.
The £2.5m-rated midfielder is stalling on a new contract with the Championship club and is keen to see where the top-flight interest leads before committing to Millwall.