Craven Cottage boss Martin Jol is keen to bolster his midfield options and Sylvestre has emerged on his radar.
Sylvestre impressed Jol during Fulham's FA Cup clashes with Blackpool, with the midfielder scoring in last week's replay at Bloomfield Road.
Championship promotion hopefuls Crystal Palace are also keen on Sylvestre.
Palace boss Ian Holloway is a big fan of Slyvestre, having signed him while he was in charge of Blackpool, and he would love to be reunited with the player at Selhurst Park to boost his side's promotion bid.
Sylvestre is in the final six months of his contract at Blackpool and his suitors know they could land the former Barcelona man for a cut-price fee.