The 30-year-old, who scored in Monday's 4-1 win at Crystal Palace, has established himself as a key player since arriving from Aston Villa in January 2011.
His current contract expires at the end of the season and he could leave on a free transfer.
But Jol wants him to stay and he has confirmed the club have already offered Sidwell a one-year deal and he could play on for longer.
Jol told the Fulham & Hammersmith Chronicle: "Of course you feel a bit worried after the game.
"They all come back and instead of one-year deals they want three years you know and this is probably no different.
"For me Sidwell can stay for two years, for example. We are talking to him and offered him a one-year deal but who knows what will happen."
Fulham's next Premier League game is a trip to Southampton on Saturday and you can see it live on Sky Sports 1 with the match starting at 17:30