The Norwegian is out of contract at the end of the season and fresh terms have yet to be agreed.
The news has alerted a host of sides across Europe to Hangeland's possible availability on a free transfer this summer.
Hangeland's representative, Rune Hauge, has confirmed talks are ongoing with Fulham, but admitted the longer he goes without agreeing a new deal the chances of him staying at Craven Cottage are receding.
"We are still negotiating." Hauge told the Norwegian media.
"But the longer it takes to reach an agreement, the chance that he will stay is decreasing.
"At the same time, Brede is happy at Fulham and the club is happy with him. We will see in one or three months."
Asked about interest from other clubs in Hangeland, Hauge said: "Yes, there have been some enquiries about what is going on."
"That includes top clubs, but no offers. We do not have permission to negotiate with other English clubs yet."