However, Fulham are not keen to offer Bullard fresh terms as he has 18-months remaining on his current deal. A number of clubs have been alerted to Bullard's situation and earlier this month Bolton failed with a bid.
Bullard Fulham from Wigan for £2.5m in 2006, but suffered a dislocated kneecap soon after arriving at Craven Cottage, and was out of first-team action until January 2008.
Tottenham, Middlesbrough and Sunderland have also been strongly linked, but now Phil Brown has made his move and he will be looking to seal a quick deal.
The Hull manager has already signed Kevin Kilbane, from Wigan, and Manchester United's Manucho, on loan for the rest of the season.
Marlon King returned to Wigan - and immediately signed for Middlesbrough on loan - and Brown believes Bullard will help kick-start Hull's season after a good start.