The England midfielder is set to quit Craven Cottage in January.
Bullard’s contract with Fulham is set to expire at the end of the season and the Cottagers have still not made a good enough offer for him.
Fulham boss Roy Hodgson said: “There might be clubs out there who can offer him that and who can match the transfer fee we think he’s worth. If it happens, it happens.”
A source close to Tottenham boss Harry Redknapp admitted: “Harry is an admirer of the boy and I’m sure will try to get him in January given the circumstances surrounding him.
“If the boy is ready to leave Fulham then Harry would have to be interested.”
