The former England international made his first foray into management in the summer of 2018, signing a four-year contract with the Gers.
He guided the club to a second-place finish in the Scottish Premiership during his first full season in charge, closing the gap on champions Celtic to just nine points.
Rangers are pushing hard to dethrone the Hoops in the 2019-20 campaign and sit joint top of the table on 29 points after 11 fixtures.
Gerrard has been tipped to succeed Jurgen Klopp in the Liverpool hot seat in the future, with the German manager recently confessing that he is planning to take a break from football when his contract expires in 2022.
However, former Reds midfielder McAteer thinks a club legend could secure a return to Anfield sooner than expected.
“Steven Gerrard made a clever move going to Rangers to begin his management career – and I wouldn’t be at all surprised if stop two on his journey is Anfield,” McAteer told the Racing Post.
“I’ve got an inkling that Gerrard will be the next Liverpool manager at the start of the 2021-22 season. I’m confident Liverpool will win the Premier League this season under Jurgen Klopp and then he’ll stick around to try to retain the trophy for another season.
“And whether he succeeds or fails, my hunch is that he’ll walk away at that point and Stevie will step into his shoes. With Stevie, he would be able to walk into a dressing room full of fabulous players and have an outstanding opportunity to continue Jurgen’s work.”
McAteer went on to suggest that Gerrard would be promised time to put his own stamp on the Liverpool squad, in the same way that Frank Lampard has been given job security at Chelsea.
“Of course, he would be given a lot of time by fans because of his reputation and his legacy,” he added. “He would certainly look at what Frank Lampard has achieved at Chelsea, where he is doing a magnificent job.
“I’m sure Frank would tell you he hadn’t expected it to go this well but he always had the cushion of knowing he had time in the bank because of his status among the fans at Stamford Bridge.”
Liverpool are in pole position to win the Premier League this season, boasting a six-point lead over reigning champions Manchester City after 10 matches.
Trent Alexander-Arnold has played a key role in Klopp’s starting XI at right-back once again, but McAteer feels he has all the attributes to covert to a midfield role.
“There are many commentators and ex-pros who believe Alexander-Arnold has a future in midfield for both Liverpool and England,” he said
“I don’t doubt that the youngster could star in the Anfield engine room. Alexander-Arnold is enjoying a stunning start to the season and is rightly earning praise for some sublime performances. Don’t forget he turned 21 only three weeks ago.”