The 31-year-old has been a mainstay in Fulham's defence since joining the club as a relative unknown from FC Copenhagen five years ago.
Hangeland's current deal runs out at the end of the season and although manager Martin Jol remains confident the Norway international will commit his future to the club, Sidwell was quick to highlight his importance to the team.
"You want to keep all of your best players," the midfielder said. "His partnership with Hughesy (Aaron Hughes) has been instrumental to the club's success throughout the past few years.
"You want to keep your best players to progress as a football club in the Premier League.
"We lost (Danny) Murphy last year skipper-wise and Brede was a natural leader on the pitch when Murph was here.
"It was natural for him to get it and obviously his presence and performances week in, week out...you very rarely see him have a bad game. We obviously want to keep him. Full stop."
Hangeland returned to the Fulham starting line-up on Monday night after a three-match suspension and helped Jol's side earn a hard-fought 2-1 win against Newcastle.
"Brede is a stalwart for the club," Sidwell added. "I'm not sure how many games he has missed in his time here.
"Obviously, when he doesn't play he is sorely missed so just having him around the place lifts the players. Having him on the pitch as well, with him being our skipper, gives everyone a buzz. Defending from the back he pushes up and I thought he was brilliant on Monday night."