Redknapp is desperate to sure up Rangers’ leaky defence that has conceded 33 goals in 19 games and sees them bottom of the Premier League table.
Redknapp has been critical of some of QPR’s high earning players this week and bringing a model professional like Hangeland to club would be a sign of intent from the former Spurs and West Ham manager.
Norwegian defender Hangeland is mulling over a contract extension at Craven Cottage as his current deal expires at the end of the season, so a move in January could be beneficial to all parties if he wants to leave.
The 31-year-old has been superb for the Whites since his arrival in 2008 and has turned down moves away from Fulham in the past.
A short trip down the road to QPR could be an option though as they will be able to offer him better wages and a longer contract than Fulham.