Steven Gerrard says the Rangers job "has all his attention" ahead of Saturday's Old Firm derby with Celtic.
Steven Gerrard says it is "presumptuous" to suggest he could succeed Jurgen Klopp at Liverpool, and claimed he has "no divine right" to manage the Premier League leaders due to his success as a player at Anfield.
Gerrard leads Rangers into the second Old Firm derby of the season on Saturday after moving to Scotland in May to take up his first senior managerial position, ending a 28-year association with the Merseyside club.
The 38-year-old failed to win a Premier League title with Liverpool - coming closest in 2014 - but the Reds are on course to land England's biggest domestic prize this season after establishing a six-point lead at the summit.
Much of the Reds' success has been attributed to the astute leadership of Klopp and Gerrard has dismissed suggestions he would be the German's natural successor when he moves on.
He told The Telegraph: "Liverpool have one of the best managers in the world and are flying high. Just because you have been a successful player does not mean you have the divine right to be next in the queue.
"Just because you are popular with the fans it does not make you the right man to replace Klopp, if and when he goes.
"It is very presumptuous. It is also disrespectful to Rangers given the size of this club and everything they have gone through to just assume I have come here to learn and use it as a stepping stone to Liverpool. I do not see it like that, although that talk is something I cannot control."
Gerrard desperate to land silverware at Rangers
Gerrard is more interested in closing the gap to Rangers' arch-rivals Celtic, the winners of the last seven Scottish Premiership titles.
"I am desperate to be successful at Rangers," he added.
"I understand the size of the club, and how much the fans want success.
"I am committed to it. I am giving everything I have got. Whether that leads to an extension here or on to a different challenge, I don't know. That would depend on the challenge. But I do not see myself as someone who will end up managing 10 or 12 different clubs, going here there and everywhere and different countries.
"Right now, I just don't see that. And this job has all my attention."
No advice from Rodgers for Gerrard
Gerrard played under his Celtic counterpart Brendan Rodgers at Liverpool, but concedes he cannot turn to the Northern Irishman for advice given the rivalry that exists between the clubs.
"As my former manager he would have been someone I leaned on just starting in management," he said.
"I think it is difficult to do that now. Look, I had a good relationship when it was captain and manager but we never socialised beyond the training ground. You would exchange texts and speak, but it was not like you went for dinner or met for coffee.
"Last week I was on the phone to Rafa (Benitez) and had a few conversations. I spoke to him for about 20 minutes, talking about certain teams. I have spoken to Gareth Southgate while doing my pro-licence. I still speak to [LFC academy director] Alex Inglethorpe quite a bit, so yes, Brendan would also have been one of those people.
"Because of the rivalry he would not want to tell me anything and I would not want to tell him anything."