Mane has a year left on his Liverpool contract and it has been claimed he wants to move on from Anfield in the summer transfer window.
Bayern Munich have been in contact with his representatives and have offered to make him one of the highest-paid players at the club.
With his contract running down, Liverpool are prepared to sell him for the right price this summer.
And according to German magazine Sport Bild, Klopp has given his approval to the sale of Mane in the upcoming transfer window.
The Liverpool manager appears to have accepted that the Senegalese will not be signing a new contract.
The German is prepared to let him go and bring a fresh face into his frontline for next season.
Bayern Munich are prepared to do a deal for a fee of around €35m and are hopeful that Liverpool will accept the price.
Mane scored 23 times last season for Liverpool and has been a huge part of their success over the years.
