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Jürgen Klopp is into his final stretch as Liverpool boss and could have just six matches left in charge, starting with the Europa League quarter-final second leg against Atalanta.
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According to The Athletic, Julian Nagelsmann is another target.
His Germany contract expires after the European Championships and he is thought to be eyeing a return to club management, with his agent claiming he has already held talks with multiple clubs.
Former Reds defender John Arne Riise believes Liverpool should be looking in the Premier League for its next manager though, and says Roberto De Zerbi would be his pick to take over.
He added: "There is always a risk of a Fergie-style decline once Klopp leaves.
"When a manager leaves, will all the players stay?
Having that connection means a lot to players, and will they stay when he leaves?
If Liverpool is looking for a talented young coach with Premier League experience, there is no one better placed.