The 26-year-old's contract expires next summer so the London club want to cash in now rather than let him play out next season then move on a free.
Fulham and Malbranque's managers have been in negotiations since last summer, and Fulham claim they have offered "the most significant financial package in the club's history."
"Unfortunately Steed Malbranque has not accepted this offer and has in fact
indicated that no offer would be acceptable at this stage as he would like to
leave Fulham next summer on a free transfer," read a statement on Fulham's website.
"The manager (Chris Coleman), with the support of the chairman and the board, is actively seeking a replacement for Steed Malbranque for the 2006-07 season and the club will listen to offers from all clubs for Steed's immediate transfer.''
Meanwhile, the Guardian has reported that Pearce is considering an approach to Chelsea to see if City can get Shaun Wright-Phillips back on a season-long loan.