The Reds’ boss worked with the World Cup winner at Borussia Dortmund, and according to the German newspaper, he wants to reunite with the versatile attacker.
Gotze – who would cost upwards of €50m – has one league goal and three assists to his name this season, but he has been sidelined for 12 weeks through injury.
When asked about the prospect of reuniting with Klopp, a smiling Gotze said, as quoted in the Liverpool Echo: “I’m under contract here until 2017. We will see what happens.
“No one has contacted me yet.”
The Reds have mustered just 22 goals in 20 Premier League games so far, so signing a goal threat could be high on Klopp’s agenda.
Gotze’s last outing, ironically, came against his and Klopp’s former side Borussia Dortmund – a game in which he scored and created a goal.
The 23-year-old claimed the dramatic winner in Germany’s World Cup triumph in 2014, and would be a major coup for Liverpool should they pull off a deal.