Hangeland has become something of a cult hero among the Fulham support thanks to his all-action displays at the heart of the Cottagers' defence.
The 31-year-old has been an ever-present in the starting line-up since he moved to Craven Cottage five years ago, but he is yet to commit himself to the west London club beyond the end of the season.
Talks about an extension began last year but both parties have so far failed to reach an agreement.
Fulham boss Jol hopes that will change soon, however. He said: "We are talking to quite a few players (about contract extensions).
"He is one of them. It's about him. But we are talking so it's a positive thing and he wants to stay here.
"That's good so there is no news now, but hopefully (there will be) in the next couple of weeks."
Mark Schwarzer, Philippe Senderos and Giorgos Karagounis are three more Fulham regulars who are out of contract next summer, and Jol would like their contracts to be extended too as their top-flight experience will prove vital if, as expected, Fulham avoid relegation.
Given that they are eight points above the drop zone, it would require a big dip in form for Jol's men to get dragged into a relegation battle, but the Dutchman is not taking anything for granted.
"We are ever so pleased to be in this situation, but on the other hand if we stay on 32 points we will be in trouble," said Jol, who takes his team to Sunderland on Saturday.
"If you look at the league over the last five or six years it's always the same situation.
"There are three or four clubs near the bottom but you always see one or two clubs getting dragged in to it and we don't want to be one of those clubs."
Although Jol possesses one of the most dangerous strikers in the league in Dimitar Berbatov, Fulham have struggled at times up front this season.
That could have been different had they beat Sunderland to the signing of Steven Fletcher, who has scored 10 times since his £12million move from Wolves last summer.
Jol concedes the Scot was on his shortlist in the close season.
"Yes (I was interested in Fletcher), but he was quite expensive," the former Tottenham manager said.
"Sunderland are well-known for getting these players in. They did that with Connor Wickham. They paid a lot of money for him. You could say Fletcher is doing well, but why shouldn't he be? He is a terrific number nine."
Jol has almost a clean bill of health for this weekend's trip to the Stadium of Light.
Simon Davies, Kieran Richardson, and Kerim Frei are all available for the game, with long-term absentee Mahamadou Diarra the only absentee from training this week.
Jol said following last weekend's win over Stoke that he feared Diarra might not play again this term, but the Fulham boss sounded more optimistic about the Mali international's fitness on Thursday.
"Diarra had a little setback a week ago, but hopefully he will be fine in three weeks," Jol said.