The 39-year-old replaced club legend Kenny Dalglish at the helm this summer, after a disappointing league campaign that saw the club finish in eighth position.
And Rodgers, who led newly-promoted Swansea to an impressive 11th-placed finish last term, has admitted that he has his work cut out.
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“[Everyone knows] the club and where it was at over the years, but we have to ask, will any club ever do that again? That’s a big question.” Rodgers told reporters.
“We have to recognise the challenge is immense - let’s be under no illusion about that.”
Whilst the Northern Irishman insists the Merseyside outfit can eventually bring back the glory days, he revealed uncertainty over whether he would be in charge when that happens.
“I genuinely think a club of our status and value to the football world, we can go again. But it’s going to take time, and whether it will be in my time, I’m not so sure," he added.
“One thing I can assure the fans though, I’m going to fight for my life – to try to get this model of play that hopefully can change the history of the club.”