Hoops manager Harry Redknapp has made no secret of his desire to sign a centre-half before the transfer window ends after Ryan Nelsen was appointed Toronto manager, with the New Zealander expected to take up his position in February.
The 31-year-old is out of contract at the end of the season, but Jol does not want to cash in on the Norway international this month.
“For us he’s a tower of strength,” said the Dutchman. “It would be silly to sell him now.”
Hangeland has made 228 appearances for the Cottagers after joining the west London outfit from Copenhagen five years ago.
Earlier in January, Jol revealed Hangeland had been offered a new deal to extend his stay at Craven Cottage, with the Dutchman urging the defender to stay.
“We will try to do everything that we are capable of to keep him,” added Jol. “There is a contract and the only thing for him to do is sign it.
“Players like Brede, if they have a decent history and are playing well for their clubs, then there will always be an interest.
“I thought he was quite happy to stay here. Of course, he wanted to know the mission of the club, who is coming in because there were quite a lot of players going out.
“There is still five months left and hopefully he will put the money where his mouth is, show everyone he is happy again and sign the contract.”