Klopp is preparing Liverpool for a make-or-break Champions League group stage encounter against Napoli at Anfield on Tuesday night.
De Laurentiis has previously claimed that he asked Klopp to manage Napoli after coming up against his Borussia Dortmund side in September 2013.
“When we played the first major European game against Borussia Dortmund, I was on the sideline and went to Klopp,” the 69-year-old said back in April.
“I asked him to come to train in Naples, he thanked me for the offer, but told me that he still had a three-year contract with the Germans.”
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When asked on Monday about his encounter with De Laurentiis and potentially moving to Italy one day, Klopp said he was only focusing on his future at Liverpool.
“I still have a three-year contract, three-and-a-half, so I am not sure if anybody wants me after that,” Klopp said. “I like Italy, I like Italian food, everything is fine. Unfortunately, I don’t speak your language that well.”
Klopp confirmed, however, that he spoke to De Laurentiis while Dortmund manager in 2013.
“I really like that Mr De Laurentiis does not hide with information and is quite chatty,” he joked.
“I don’t think I told anybody about that talk but he mentions it from time to time. I think he is happy with all the choices he made in past.
“Bringing Maurizio Sarri in was incredible and now bringing Carlo [Ancelotti] back is outstanding. I think they are really happy with the coaches they had and have. At the moment the people here are happy with me as well so we don’t have to think about changing.”
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