Hangeland has impressed after joining Fulham from FC Copenhagen 18 months ago and has been linked with a summer move to Arsenal.
“We’ll do everything in our power to keep Brede,” Hodgson was quoted as saying in The Sun.
“Everyone knows he’s a player that we love. He’s still contracted to us and we want to keep him.
“We’re doing everything in our power – but our power sometimes can’t be compared to the power of other clubs.”