Steven Gerrard has admitted it is his "dream" to become Liverpool manager one day but says he hopes Jurgen Klopp remains in charge "for many years".
Former Liverpool captain Gerrard has steered Rangers to their first Scottish Premiership title in 10 years, just three years after taking on his first managerial role at Ibrox.
His success in Scotland comes while Klopp is enduring the toughest spell of his six years as Liverpool boss, with his side eighth in the Premier League and without a home win since December 16.
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But speaking to ITV, Gerrard said: "The Liverpool fans don't want me to be the manager of Liverpool Football Club. They want Jurgen Klopp to continue to be the Liverpool manager, and I'm totally with all of them.
"We shouldn't talk about this, we have one of the best managers leading our club at the minute. I love him.
"I hope he stays for a few more years. But I've got a job here. I don't think it's helpful to talk about this and I hope Jurgen stays at Liverpool for many years."
Gerrard made 710 appearances and won nine trophies for Liverpool during his 19-year playing career before an 18-month spell in the US with the Los Angeles Galaxy.
After hanging up his boots, Gerrard took on a role as a youth coach at Liverpool before becoming Rangers boss in May 2018.
"Liverpool is my club," he added. "I had a great journey. Is it a dream for me to one day be the Liverpool manager? Yes, it is, but not yet and who's to say I'll ever be good enough.
"There's a lot of fantastic managers that would all like the chance to manage Liverpool. We need to respect Jurgen first and foremost."
Gerrard: Title not about making up for Liverpool lows
Gerrard is reluctant to compare winning the Premiership title win with his achievements as a Liverpool player, and insists it is not about him making up for any "highs or lows" he experienced at Anfield.
"To be honest I haven't really had time to reflect and think about the last two days, or compare it to other achievements in my career," said Gerrard.
"I don't think it's fair to compare achievements. What I achieved as a player was fantastic, of course it was, but I'm on a different journey, on a different career path with a different club.
"It's not really about me, from a personal point of view, and me making up for previous highs or lows. It's about Rangers, it's about achieving our first massive goal together.
"It's all about the players and supporters. I'm extremely proud of both."
'Rangers have major respect for Slavia Prague'
Gerrard's attention will now turn to the Europa League, as Rangers travel to face Slavia Prague in the first leg of their last-16 tie on Thursday.
The Czech side knocked out Premier League high-flyers Leicester in the previous round and Gerrard is wary of the threat posed by Jindrich Trpisovsky's side, who are also on course to win their own domestic league this season.
"I think Slavia's performance over both legs was extremely strong," added Gerrard.
"Leicester are a very good team with a good coach, who have so far had an excellent season. Instantly it made you well aware of the size of the challenge that we're going to face.
"This is a team that is going extremely well domestically.
"We've got major respect for the opposition, for the players, for the coach, and we know that we have to be at our maximum, in terms of our performance, to get this job done."