Jurgen Klopp Manager Profile
Clement, now manager of Derby County, was assistant to Ancelotti at the Bernabeu up until the summer.
He also coached under Ancelotti when the Italian was in charge of Chelsea between 2009 and 2011.
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Klopp, 48, has won two Bundesliga titles and got Borussia Dortmund to the Champions League final.
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He quit the German outfit in the summer and is said to be keen on taking up the post on Merseyside.
Ancelotti, meanwhile, has won titles in Spain, Italy, France and England (with Chelsea in 2009/10), has won the Champions League three times and the FIFA Club World Cup twice.