Benitez announced last week he would be leaving the Serie A outfit.
The former Chelsea and Liverpool boss is widely expected to replace Carlo Ancelotti, who was sacked by Real Madrid.
Klopp is much fancied to take over the reins at Anfield, should Reds chiefs sack Brendan Rodgers.
Next season Klopp will be training in the South of Italy, at Napoli
Franz Beckenbauer
However, it is thought Klopp would want the existing transfer committee to be scrapped should he take over.
But Beckenbauer is convinced Klopp will become the next Napoli boss.
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Jurgen Klopp blows a kiss to the Dortmund supporters
"Next season Klopp will be training in the South of Italy, at Napoli," Beckenbauer told Sky Sport Deutschland.
Klopp saw his side lose 3-1 to Wolfsburg in the German Cup final last night.
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