Rangers, beaten 5-0 by Celtic on Sunday, are in disarray but Gerrard, who has no first team managerial experience, is likely to be offered the job.
Rangers added that Murty "will take some time to consider his options, which include returning to his role at the Rangers Academy".
The assistant coaches Jimmy Nicholl and Jonatan Johansson will take charge of the club's three remaining Scottish Premiership fixtures, starting with Kilmarnock's visit to Ibrox on Saturday.
Rangers are hopeful that they will be able to convince Gerrard to move north of the border and take charge of the club in the summer.
And Rodgers is adamant Murty has been treated "discourteously" by Rangers after he stepped up to the top job for a second time following the sacking of Pedro Caixinha and the failure to land Aberdeen's Derek McInnes.
But he ended up staying in the post for six months as chairman Dave King and his board dithered over appointing a new long-term successor.
Gordon Strachan has warned Steven Gerrard the pressure of managing Rangers would be like nothing he's ever experienced.
The build-up to Sunday's match then saw Murty undermined by Rangers entering into talks with Champions League victor Gerrard.
The defeat at Celtic Park came just two weeks after the Ibrox side had lost 4-0 to Brendan Rodgers' team in the Scottish Cup semi-final at Hampden Park.
The Glasgow giants lie third in the Premiership table with three games of the season remaining, with only goal difference separating them from fourth-placed Hibernian.
He also took over between the sacking of Mark Warburton and the appointment of Caixinha past year.
Rangers, now third in the league standings, next face Kilmarnock on Saturday.