Fulham are coach-less after Felix Magath was sacked on Thursday, with the London side bottom of the table after seven matches following their relegation from the Premier League.
Kit Symons was appointed on a caretaker basis as Fulham search for Magath's successor but Murphy has thrown his hat into the mix.
Murphy, who spent five years at Craven Cottage, told BBC Radio 5 Live: "I care about the club deeply and I've always had a desire to get involved but that's out of my hands.
"I've always said I'd like to go back to Fulham at some point in some capacity because I have an affinity with the supporters there.
"If they did want to speak to me, of course I'd be open-minded to that. I would never disregard something like that."
Murphy made over 160 Premier League appearances for Fulham, while the former England international captained the club in the 2010 UEFA Europa League final against Atletico Madrid.
