Sidwell has been in good form for the London club, having played every game in their Premier League season so far. The midfielder also scored in the club's recent 4-1 victory over Crystal Palace.
"Of course you feel a bit worried after the game [when he plays like that]," FourFourTwo quotes Jol as saying.
"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 have endured a less than positive start to the season, but now find themselves 14th in the Premier League following their win on Monday night.