Tottenham and Liverpool are leading the chase to sign Malbranque after the Frenchman ruled out the prospect of playing for Aston Villa.
Villa boss David O'Leary tabled a bid of around £3.5m, but Malbranque said he had no interest in joining them.
Malbranque arrived at Fulham from Lyon for £4.5m, four years ago.
Liverpool and Spurs are both expected to make bids for Malbranque in the next few days.