Sidwell's current contract with the Cottagers expires at the end of the season and he could leave on a free transfer.
The 30-year-old, who scored in last weekend's draw with West Brom, has established himself as a key player since arriving from Aston Villa in January 2011.
Fulham boss Martin Jol is a big admirer of Sidwell and is hopeful he is will sign a new contract.
"He's done well," Jol told the Fulham Chronicle. "We're talking to him to extend his contract.
"I think he wants to stay."