Zamora, the man who scored the goal against Preston to take the Hammers back to the Premiership, had limited first team action last season following some minor injuries and John Pantsil has only played a handful of games since arriving two year ago.
Alan Curbishley is under pressure to reduce the wage bill before any new additions can be made to the squad and it seems Fulham are willing to part with around £6 million to bring the duo the Craven Cottage
A statement of the official site reads,
"West Ham United can confirm that the club has received an approach from Fulham for the transfer of Bobby Zamora and John Pantsil.
"The club is 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 said: "We recognise that Bobby Zamora and John Pantsil have had limited first-team opportunities last season at West Ham United. 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."