The midfielder left Wigan to join Fulham in a £2.5million deal two years ago, but is wanted back at the JJB Stadium.
The 29-year-old suffered a serious knee injury just four games into his Fulham career and did not play a first-team match for 16 months.
Cottagers boss Roy Hodgson is now facing a battle to hang on to the fans favourite Bullard following the approach from his former club.