The deal for Sadio Mane was turned down by the Reds.
The German club came back with a new offer after the initial one was turned down.
Liverpool are understood to want about €50m (£42.8m) for 30-year-old Mane considering Bayern's similar valuation of 33-year-old Robert Lewandowski.
They have one year left on their current contracts.
The Poland international is moving to Barcelona this summer.
He hasn't said much about his future. At the weekend, the forward joked that the majority of the people in his homeland would prefer him to leave the club.
He has promised a special answer over his future.
Since arriving from Saints in June 2016 for a fee of £36m, he has scored 120 goals for the Reds, helping the club to win the league and the cup.
He extended his contract with the club at the end of last year.
There is a dilemma over the future of Egyptian star Mohamed Salah, who will be a free agent in Summer 2023.
Barcelona are said to be interested in signing him as a free agent at the end of the season, despite the fact that he intends to stay atLiverpool.
On Wednesday, Liverpool were linked with a bid for 22-year-old Uruguay and Benfica striker Darwin Nunez.
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