Gerrard has captained England in the absence of the injured Rio Ferdinand and will lead England out again for Tuesday's Euro 2012 qualifier in Basel, Switzerland.
But Murphy, currently captain of Fulham, has urged Fabio Capello to consider handing him the armband on a permanent basis.
"I believe there is the strongest possible case for Steven carrying on, regardless of Rio's fitness," Murphy told the Liverpool Echo.
"He leads by example, as he has shown in the last two games, and is the best player in the England team. He is emerging as our real leader.
"He carried the armband through the World Cup and has been a real inspiration in the two opening games. There is no one better for the job. This is not me having a pop at Rio in any way.
"He has done absolutely nothing wrong but, given his unfortunate injury record, he will be grateful to be back in the squad. Just being named in an England party again will be plenty for him to be going on with."