The 36-year-old retired from professional football in November after ending an 18-month spell at MLS outfit Los Angeles Galaxy before the end of last year.
Now learning the ropes as a coach at Liverpool's academy, Gerrard has been tipped by Rush as a potential key element in a "new Anfield dynasty".
The Welshman told The Mirror: "At the moment, there's no better man for the job than Jurgen Klopp. But, maybe, in the future we can start a new Anfield dynasty, with Steven Gerrard and Jamie Carragher calling the shots. Maybe that's what we're missing at the moment.
"Stevie G has the perfect pedigree to, one day, take over as manager. He joined the club as a kid, was brought into the team by Gerard Houllier, has captained the side, been the club's best player for years. So the stage is set — if he wants it. The fans would love it.
"He also knows the importance to the supporters of bringing good local talent through. We've got some good foreign players in the squad, but fans love to associate themselves with their own – players such as Stevie G, Jamie Carragher and Robbie Fowler."
During his 17 years at Liverpool, Gerrard won two FA Cups, three League Cup trophies and the Champions League.