The 31-year-old has been a mainstay in the Cottagers' defence since joining the club as a relative unknown from FC Copenhagen nearly five years ago.
There is, though, talk that Hangeland's time in west London could be coming to an end, with the Norway international's contract expiring at the end of the season.
His agent Rune Hauge last night said they were in no hurry to sort out a deal and that there is interest from other clubs in England and further afield.
However, that is not something concerning manager Jol, who remains confident of striking a deal with Hangeland.
"I have been in this job a long time," he said. "I have over maybe 1,300 games as a player and as a manager.
"Maybe a long time ago I would be worried a bit but I stopped worrying. I always worry about the next game, that is my only little concern.
"Rune is a good guy so if we can strike a deal then we will do that.
"He loves it here so it would be a bit strange if he goes to another club because he loves it here. He is team captain.
"I don't think he will find a better club than we are and if he does he is entitled to go wherever he wants.
"But I still feel that we have a big chance of keeping (him) here."
Hangeland's departure would be a huge blow for Fulham, who have to only look back to Monday for an example of his importance.
After three matches out suspended in which the Whites managed to collect just one point, the defender shone in the 2-1 defeat of Newcastle.
"Brede is my captain, he is club captain, team captain," Jol said. "He has been important for as long as he has been here.
"I told him this morning that he looked hungry, he looked eager, ambitious, you know?
"Of course we missed him for three matches but he probably needed that space and he came back and he was better than ever before."
Hangeland will almost certainly start again on Saturday as Fulham look to make it back-to-back victories at near neighbours QPR.
Mahamadou Diarra is a major doubt after he took a knock against Tottenham two weeks ago, while Simon Davies is not ready to feature despite returning to training after a long-term hip injury.
But while fully-focused on the trip to Loftus Road, Jol has half an eye on new additions for January.
Dnipro's Derek Boateng and PSV midfielder Atiba Hutchinson have been mentioned as potential additions, while the Dutchman today laughed off talk of a move for Manchester City's Mario Balotelli.
It was reported earlier in the week that the Italian had driven to Jol's house to meet with the agent both share, Mino Raiola.
Asked if a move for Balotelli could be on the cards, Jol said with a smile: "Mino, my friend, said that Balotelli is probably as expensive as the Mona Lisa, the painting.
"You know how much that costs? It will probably be impossible for us.
"I have got to wait until he is probably 30 or 31. Then there might be a chance.
"Zlatan Ibrahimovic, who was with my friend as well, could be 34 or 35 so you will have to wait a bit."