The Cottagers are ready to offer Zamora the most lucrative contract in the club's history to ward off interest from potential suitors.
The likes of Liverpool and Birmingham were credited with an interest in the England international on transfer deadline day, but Fulham managed to snub their overtures.
Fulham assisant boss Mark Bowen has confirmed contract talks are ongoing and the club were hoping to tie up a deal soon.
"What I know is that he is currently in discussions with the club over a possible new deal," Bowen said.
"It has been ongoing for a few months and obviously way before Mark (Hughes) and I came in.
"But my understanding is that we are hopeful Bobby will agree a long-term contract with the club."