The 30-year-old, who has played every minute of Fulham's Premier League campaign, scoring twice in his eight matches, is out of contract at the end of the season.
|11/2||Steve Sidwell is 11/2 with William Hill to score anytime against Southampton|
"Of course you feel a bit worried after the game [when he plays like that]," Jol said, referencing Sidwell's spectacular volley against Crystal Palace.
"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 travel to Southampton on Saturday looking to post their third successive Premier League win, and Jol is confident of picking up a good result despite their opponent's excellent start to the campaign.
"Southampton are a strong team but we have done our research and have hopefully found a few weaknesses," the Dutchman added.
Fulham defender Fernando Amorebieta acknowledged the threat that Southampton will pose, but is also buoyant ahead of their trip to St. Mary's Stadium.
"Southampton are a team that does things very well," Amorebieta told the club's official website.
"They've conceded very few goals but hey, I think we're entitled to take confidence from the win against Crystal Palace and go to Southampton full of enthusiasm and a will to win."