Everton boss David Moyes has confirmed Leroy Fer is currently undergoing a medical with the club, but is remaining cautious until the deal has been fully completed.
The Toffees agreed a fee in the region of £8.5 million with FC Twente for the highly-rated 23-year-old midfielder, with Moyes looking to add to his squad and boost the club's attempts to secure a Champions League spot.
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West Brom's Jonas Olsson and Porto's Rolando have also been on Redknapp's radar this month as he attempts to plug the gaps in his squad left by the exits of Ryan Nelsen, who has been appointed the new manager of MLS side Toronto, and Anton Ferdinand, who has joined Bursaspor on loan.
Hangeland's current deal expires in the summer and he has indicated to the club that he will commit to the extended terms, which would bring him in line with top earners Mark Schwarzer and Dimitar Berbatov.
But the Norway international, who turns 32 in June, can sign a free transfer pre-contract agreement with a foreign club before Thursday night's deadline or push for a move to Loftus Road.
Nevertheless, the experienced defender, who joined Fulham in January 2008, is understood to be settled at Craven Cottage and unlikely to follow former colleagues Bobby Zamora and Andy Johnson to Loftus Road.
Manager Martin Jol has said that he is "optimistic" that Hangeland will take up the "good" offer made by the club.
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