The Reds confirmed the signing of the 16-year-old on Sunday after Liverpool FC reached an agreement with Championship side Fulham for their home grown talent.
The England Under-16 international made his Fulham debut aged 15 years and 174 days in the League Cup in September 2018.
Elliott became the youngest-ever player to make his Premier League debut when he came off the bench against Wolves at the age of 16 years and 30 days.
Liverpool FC won the race to sign the highly-rated Fulham teenager despite reported interest from some of the top clubs in both the German and Spanish top flight.
And Klopp has already been impressed with Elliott after the new signing linked up with the Liverpool FC squad on Sunday following his move to the Champions League holders.
“I could say so many positive things about the boy,” Klopp is quoted as saying by Metro.
“We signed him, he came here, he decided on us and could have gone pretty much everywhere but he wanted to be part of Liverpool.
“The stories with the boy start early and already he is the youngest ever Premier League player and has broken quite a few records because of his talent.
“Now he is here so let’s work with him. He needs game time, we will see where he gets that but he is obviously a fine, fine footballer and that’s why we were really interested in signing him.”
Elliott is the second summer signing at Liverpool FC after 17-year-old Dutch centre-half Sepp van den Berg secured a switch to the Reds from FC Twolle in July.
Liverpool FC will be hoping to take the final step and win their first Premier League title this season after the Reds finished in second place last term.
Klopp’s side ended up a point adrift of champions Manchester City despite losing just one game.
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