Newcastle are one of a host of Premier League clubs interested in the Norwegian centre-back who has impressed in his time at Craven Cottage.
Manchester City, Arsenal and Tottenham have also been tracking the 27-year-old but Hodgson is determined to keep him in west London.
"We have had plans for a while to talk to him - a) about an extension and b) about improving his contract. That's in hand," Hodgson said.
Hodgson is confident Fulham will do all they can to persuade him to remain at Fulham but concedes that he may have to look elsewhere should a big-name club come calling.
"If it happens, it happens and we will deal with it the best we can," Hodgson said.
"But in the meantime Brede and other players who might interest other clubs are still here and we will do our best to keep them."
Hodgson wants Hangeland to form the back-bone of his side which is still challenging for a place in the new Europa Cup next season.
Last night's last-gasp 1-0 defeat to Hull did not help their quest and Hodgson wants his side to recover ahead of Manchester United's visit in the FA Cup sixth round on Saturday.
"Of course the team will now need lifting for United," he said. "There's no worse way to lose a game than to play well, stare at a 0-0 draw when you think we should have scored and then to lose in the 92nd minute.
"You couldn't write a worse scenario for a player or coach than that. This is the ultimate football nightmare that you have to live through."
Hodgson and Fulham will also investigate claims made by John Paintsil that he was abused towards the end of the match.
"The referee said to me that John complained to him about being abused by somebody," Hodgson said. "The referee didn't hear anything so he couldn't take any action. I'll investigate it with John.
"If John feels we as a football club need to do something about then we'll explore it."