The American is growing frustrated with his playing time at Stamford Bridge.
Pulisic made just his third start of the season against Juventus on Wednesday, with injuries also playing a role in his lack of minutes.
Klopp tried to sign Pulisic in 2019 before he agreed to join Chelsea.
However, El Nacional reports that the Blues will not sell Pulisic to their Premier League rival.
Barcelona are also interested but are unable to afford the £42m asking price.
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