The 27-year-old has been a hit at Fulham this season and has also been linked with a Arsenal and Liverpool.
Fulham boss Roy Hodgson admits he faces a struggle to keep the Norwegian defender at Craven Cottage.
“Everyone is talking about Brede and I would say that he has certainly got the capacity to play for any of the top four clubs,” said Hodgson.
“But there is no reason not to be optimistic that we can keep this unit together through January.
“I am hoping he might be one of those who is satisfied with playing in what, in my opinion, is quite a good team in The Premier League and that he is not looking necessarily for that extra move.
“My other hope is there won’t be that much money around in the transfer window, because it is pretty obvious that his value to this club is very high.
“But I cannot stand here and guarantee that Hangeland – or Jimmy Bullard, for that matter – will not go because you do not know what type of situation you are going to find yourself in.”