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He has remained coy about any potential move to Anfield, revealing this week that his family want him to remain in Portugal.
That has opened the door for other alternatives with The Athletic reporting that Germany boss Nagelsmann was a potential option.
It is believed that Liverpool's data analysts have drawn up a list of candidates based on various criteria, with the 36-year-old scoring highly.
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But it has now been confirmed that Nagelsmann will stay on as Germany boss past this summer's European Championships.
His contract had been due to expire after the tournament, fueling speculation over a potential return to club football.
Bayern Munich was also said to be keen on re-hiring Nagelsmann having sacked him a year ago.
The Reds boss plans to take at least a year out from football when he leaves Liverpool at the end of the season.
Last month, SportBILD reported that the German FA would approach Klopp if Nagelsmann departed, in an attempt to lure him back into management ahead of the tournament in the US, Canada and Mexico.
Brighton boss Roberto De Zerbi also remains a candidate for the Anfield job, with Liverpool believed to be carrying out extensive research on a number of options.
But according to CaughtOffside, Bayern could now turn its attention to the Italian.
Liverpool.com says: It appeared that Nagelsmann was set on a return to club football but he has put speculation to bed.
His decision to stay on with Germany means if Klopp is to return to management in a year's time, it will be at a different club.
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