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After the Reds were knocked out of the Europa League despite beating Atalanta 1-0 in Bergamo, there are now little more than a handful of Premier League fixtures remaining for the German before he takes a break.
Klopp's final matches are as follows: Fulham (A), Everton (A), West Ham United (A), Spurs (H), Aston Villa (A), Wolves (H).
Only perfection will be enough to win the Premier League title and even that might not be sufficient for the Reds because Manchester City has moved into the ascendency.
Amid the final knockings of Klopp's tenure, the search for his replacement is ongoing behind the scenes.
Sporting CP head coach Rúben Amorim became the leading contender for many once Xabi Alonso ruled himself out of the running, but the 39-year-old Portuguese is not the only option that Michael Edwards is assessing.
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Julian Nagelsmann, who is one of the most highly-rated young coaches around, has appeared on some shortlists, but the Germany boss was always going to be a tricky candidate to bring in because he would only arrive after the summer's European Championship, which ends only a month before the new Premier League season begins.
But he has now decided to sign a contract extension.
Nagelsmann has agreed an extended contract and will remain in position with Germany until after the World Cup in the US, Mexico and Canada in 2026, despite links with Bayern Munich and others.
Roberto De Zerbi is not thought to be among the leading contenders despite the job he has done with Brighton but the Italian is the second favorite (after Amorim) with the bookmakers.
He might not want the distraction of proper talks until the Portuguese title is wrapped up, but Amorim should be considered the leading contender right now.
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