Hangeland's contract expires at the end of the season and no new deal has been agreed as yet.
A number of clubs are thought to be monitoring Hangeland's situation with the big defender able to talk to interested clubs in January.
Fulham are hopeful of keeping hold of the Norwegian and Sidwell insists it vital they keep hold of the likes of Hangeland if they want to progress.
"You want to keep all of your best players to progress in the Premier League," said Sidwell.
"Brede is a natural-born leader and, if you look at his performances week in, week out, he very rarely has a bad game for us.
"His partnership with Aaron Hughes has been instrumental to the club's success throughout the past few years. We want to keep him here.
"Brede is a stalwart and when he doesn't play he is sorely missed.
"Just having him around the place lifts the players and having him on the pitch, being our skipper, gives everyone a buzz."