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That's according to Liverpool legend Mark Lawrenson who believes managing Liverpool is on a "different spectrum" to Rangers.
Gerrard, 40, has been linked with a sensational return to Anfield this summer following his managerial heroics in Scotland.
Congratulations from all of us at #LFC to Steven Gerrard and his team on winning the Scottish Premier League title- Liverpool FC (@LFC) March 7, 2021
But Lawrenson has pumped the brakes on Gerrard potentially replacing Jurgen Klopp at the end of the season amid Liverpool's disastrous run in the Premier League.
He told the BBC: "There has always been the issue of whether Steven will manage Liverpool or not. Due to Liverpool's poor season, everyone is saying 'Steven will be next, Steven will be next', so that shout has grown louder.
"What I would say is that, for all the success at Rangers, managing Liverpool is on a different spectrum. It would be a massive step. It would be a big gamble for the club's owners - Fenway Sports Group - to appoint him.
"I think the one-eyed Liverpool fan would be saying 'Get Stevie G in' if Jurgen Klopp were to leave, but I think others would take a step back and go: 'he's done an absolutely fabulous job at Rangers, he was a great player, but maybe he would need to take another job in the Premier League first.'
"I also don't see Klopp going anywhere. He has been as close to Bill Shankly as the club have ever had, he won't be losing his job anytime soon."
The 63-year-old added: "The trouble for Steven then is that other managers who have moved on from their first job as a stepping stone to something bigger end up not having the same success, so he has to be very, very careful.
"He'll already be thinking about winning the Premiership again next season and the chance for a shot in the Champions League with Rangers will be at the forefront of his thinking too.
"But, in the unlikely event that Liverpool come calling this summer, Steven could not say no. Because you won't get asked twice."
Gerrard, who has been at Rangers since 2018, bagged his first piece of silverware as a manager last weekend.
Could Gerrard take over from Klopp? Let us know what you think.