"The club are looking forward to an exciting new season with a fully-fit squad, including the return of Kieron Dyer and Craig Bellamy along with Dean Ashton secured on a long-term contract.
"Added to the form of Carlton Cole and the emergence of Freddie Sears, the decision has been made to let Fulham speak to the two players."
West Ham United CEO Scott Duxbury added: "We recognise Bobby Zamora and John Pantsil have had limited first-team opportunities last season.
"They want to play regular first-team football and we have given permission for them to speak to Fulham with a view to concluding a move."
