The veteran midfielder's current deal at Craven Cottage is due to expire in the summer.
However, the 35-year-old has admitted that he would be happy to extend his stay with the Whites.
"I have spoken to the club a couple of times but there's no great urgency with me because I'm happy and they are happy with me," Murphy told The Sun. "I'd be surprised if it didn't get sorted."
Murphy joined Fulham from Tottenham Hotspur in 2007.