The Germany playmaker has been linked with the Reds for much of the summer transfer window as his future with Bayern Munich seems uncertain.
But The Echo have reported that manager Jurgen Klopp - who helped to devleop him at Borussia Dortmund - is not interested in bringing the 23-year-old to Anfield.
Earlier this month Klopp wrapped up a £30 million deal for Sadio Mane and the report goes on to claim that the German manager is happy enough with his attacking options.
The Echo has suggested that Liverpool's exit from the race means that Tottenham Hotspur and Dortmund will now battle for the £20 million schemer.
Tottenham might be handicapped by the fact that Dortmund played such a big role in helping to establish him as a prominent figure in the game, but he did quit the Signal Iduna Park outfit once already and Klopp's absence means he may not be as willing to return.
But if Klopp is not keen on re-signing him then Spurs might feel optimistic in their pursuit, with Bild reporting at the weekend that his father and Tottenham delegates had already met with one another.