The Poland international signed for Barcelona last summer after telling Bayern Munich that he wanted to leave, eventually moving to the Camp Nou for £42.5million.
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But Klopp would have loved to have brought him to Liverpool and even tried to persuade the striker to join him at Anfield in 2017 but to no avail.
The duo know each other well as a result of their time together at Borussia Dortmund, where Lewandowski scored 102 goals and grabbed 42 assists in 186 games under his management.
Liverpool travelled to Germany in the summer of 2017 and Klopp would meet his old talisman again but his attempts to persuade him to join the Reds did not go to plan.
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"We hosted Liverpool FC with Bayern in the Audi Cup in Munich in 2017," Lewandowski said to BILD.
"We spoke on that occasion. Klopp asked me, 'Don't you want to come to Liverpool?' We looked at each other, then I laughed.
"I don't know if he was totally serious. But going to Liverpool was never in my mind."
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Lewandowski had just completed his third season at Bayern Munich, where he was the main man and bagging goals for fun.
The season before, the forward netted 43 times in all competitions while Klopp was entering his third year in charge of Liverpool who were still finding their feet under the German.
They finished fourth in the Premier League but crashed out of the FA Cup and League Cup and weren't as attractive a destination for a striker in the peak of his powers.
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Lewandowski would go on to play another four years at Bayern Munich where he made a total of 375 appearances and scored 344 times.
His goalscoring exploits have hardly slowed down, despite reaching the age of 34, and he has netted 27 times in 34 matches this season for Barcelona.
Liverpool found their feet under Klopp despite ultimately being rejected by Lewandowski in 2017 and have since won the Premier League, Champions League, FA Cup and Carabao Cup.
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However, they have struggled so far this campaign and have crashed out of every competition with Klopp's best chance at a successful season now being a top-four finish in the table.