The former Man City winger joined the German champions in 2020 for a fee of £55m but only started 22 league games last season.
The report states that Sane's game time at Bayern could be affected due to the arrival of Sadio Mane and he is seriously considering leaving the Bundesliga.
The fee that would unlock a move to Anfield is said to be around £46m and Klopp is said to be a big admirer of the winger
Sane spent 4 years in Manchester and in that time he won every domestic trophy there is to win in England, as well as earning himself the PFA young player of the year following City’s record-breaking 100 point season in 2017/18.
Whilst it would be strange to see Sane in a Liverpool shirt, there is no doubt that the German would thrive under the influence of Jurgen Klopp on Merseyside
The Reds have had one of the most dangerous attacks in world football over the past few seasons, but the departures of Sadio Mane, Divock Origi and Takumi Minamino have left them looking sparse in depth.
Diogo Jota’s hamstring issues have left Liverpool with only two outright wingers in Luis Diaz and Mohamed Salah.
However, having already spent £85 million on Darwin Nunez, it is unlikely that the Reds would be willing to spend so much for Sane.
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