The Scottish club have held talks with the former Reds captain as they look to take him to Ibrox, and are ready to offer the 37-year-old the job.
Gerrard, who is currently in charge of Liverpool's U18 side, is understood to be weighing up the approach, but has made no secret of his desire to get into senior management.
Some bookmakers suspended betting on Thursday on Gerrard replacing Graeme Murty as Rangers boss. Gers chairman Dave King was spotted at Anfield on Tuesday night, watching Liverpool beat Roma in the Champions League semi-final.
Gerrard, too, attended as part of BT Sport's punditry team, and was present at Ibrox for last month's Old Firm clash with Celtic. His Liverpool youth team visited Rangers earlier this season for a friendly match.
"I'll never forget when I'm invited to Ibrox," Gerrard said afterwards. "It's an iconic stadium. I've got a lot of respect for this football club and it's history and tradition - and that's the reason why we took the invitation up.
"I had to take the opportunity to bring my team up to experience playing in front of that stadium, just being in the surroundings, in the dressing room - it's a wonderful place."
Rangers are in the market for a new manager with Murty unlikely to be given the job on a full-time basis. The former Reading defender was installed on a caretaker basis following the sacking of Pedro Caixinha in October, and has kept them second in the SPL table - albeit comfortably behind leaders Celtic.
Their 4-0 defeat to their fierce rivals earlier this month in the Scottish Cup semi-final led to protests from supporters, who are desperate for a change in mentality at the club.
Should Gerrard make the move, it will raise the tantalising prospect of him going head-to-head with Brendan Rodgers, his former Liverpool manager. Rodgers has enjoyed blanket success since moving to Scotland in 2016, winning the domestic treble last season and closing in on a repeat this time around. Gerrard's job would be to stop the Hoops' dominance.
The former England star has impressed since taking a role at Liverpool's Academy in January 2017. Having been appointed as U18s manager last summer, he has settled nicely into the job. His team sits third in the Premier U18 League table, while they reached the quarter-finals of the UEFA Youth League, losing agonisingly on penalties to Manchester City.
Furthermore, a number of his players have moved up the ladder this season, with the likes of Curtis Jones and Rafael Camacho featuring on the bench for Jurgen Klopp's senior side in recent weeks. Others have stepped up to U23 level with Neil Critchley.
Gerrard himself has not hidden his desire to move into mangement. He turned down the chance to become MK Dons boss before taking the role with Liverpool, and has been linked with other Football League vacancies since.
“I want to improve and I want to coach at the top level,” he said back in December, while in a recent interview he reiterated that desire.
“I feel like I’m a man on the move," he told JOE.co.uk. "I don’t want to stand still for very long. I want to progress, I want to improve, I want to keep testing myself.
“There’s no timescale on this, but I certainly want to coach at the top."
His first opportunity could be about to arise. Gerrard vs Rodgers for glory in Scotland? It sounds intriguing.