But Spanish newspaper Sport claim Klopp has asked his board to make an approach for Jese, as the German believes the Madrid ace can solve the Reds goalscoring problems.
The Spaniard will be available for £23.2 million and Liverpool are willing to meet Madrid's valuation.
Jese has spent his entire career at the Santiago Bernabeu, playing 74 first-team games.
He has scored 14 goals and registered 11 assists for the club, as well as being capped five times at Under-21 level for Spain.
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