Gerrard, currently coach of the under-18 side at Liverpool’s academy, tops a shortlist of contenders to take charge of the Ibrox club this summer, compiled by Rangers chairman Dave King, director of football Mark Allen and managing director Stewart Robertson over the past few weeks.
It is understood any appointment is not imminent but King and his colleagues are hopeful they can persuade Gerrard to take his first step into management at Rangers.
The 37-year-old, who brought his illustrious playing career to an end in 2016 after a stint in Major League Soccer with LA Galaxy, has been coaching at Liverpool since February 2017 and previously turned down the chance to become manager of MK Dons.
If Gerrard accepts the opportunity to manage Rangers, he would find himself going head to head with Celtic manager Brendan Rodgers, one of his former bosses at Liverpool.
Scotland manager and former Rangers boss Alex McLeish believes Gerrard, although untested in management at senior level, has obvious qualities to bring to the role.
“Steven knows the game inside out,” said McLeish. “With regard to coaching, I am sure he has got some things to learn. He won’t have all the answers to that but I am certain he is somebody who could be a great man manager.
“I hear the way he is coaching the kids and giving them the Liverpool values and what it takes… sometimes that gets missed in the process of growing up – that passion and enthusiasm for every game. The kids at Liverpool have got a good leader in there.”
With four league games left under Graeme Murty, who replaced the sacked Pedro Caixinha on an interim basis in October and was then handed the reins until the end of the season, Rangers are battling to secure runners-up spot ahead of Aberdeen and Hibs.
They face a trip to Celtic Park on Sunday when victory for Rodgers’ side would see them wrap up a seventh consecutive title win.
Rangers are already revamping their squad ahead of next season and expect to be in a position to confirm the pre-contract signings of goalkeeper Allan McGregor and midfielder Scott Arfield within the next 24 hours.
Scotland international McGregor is understood to have agreed terms on a return to Rangers, having left Ibrox in the summer of 2012, despite receiving an offer to remain with current club Hull City. The 36-year-old is expected to have a medical today.
Former Falkirk and Huddersfield player Arfield, out of contract at Burnley, is also in advanced talks with Rangers. The 29-year-old Canada international is ready to sign a three-year contract.
Burnley manager Sean Dyche confirmed Arfield would be moving on at the end of the season.
Dyche said: “He was a boyhood Rangers fan and that one’s pretty simple if they want to speak to him. Scott’s a player who has done a lot for this club. We hope things work out in his favour.”