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.
Liverpool have already spent £29m on a Bundesliga sensation in recent times, but Roberto Firmino has flattered to deceive since his move from Hoffenheim.
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 scored the winning goal in Germany’s World Cup triumph in 2014, and would be a major coup for Liverpool should they pull off a deal.