The 33-year-old midfielder wants to finish his career at Fulham. He has one year remaining on his contract at Craven Cottage - and there could be more if he keeps pace in the Premier League next season.
It would be the perfect platform for the Fulham captain to bow out after a successful career, in which he won a unique treble with Liverpool in 2001 of League Cup, FA Cup and Uefa Cup.
Murphy said: "I hope this is my last club. I've got another year after this and I'm feeling all right."