Both broadcaster Sky and top-selling daily Bild say the clubs have agreed a transfer fee of €32-million ($33.5m) plus up to nine million in bonuses.
Mane is set to receive a three-year contract.
The 30-year-old could replace Bayern’s Poland star striker Robert Lewandowski, who has repeatedly said he wants to leave and has been linked to Barcelona.
Sadio Mané has reached full verbal agreement with Bayern on personal terms. Three year contract ready – talks will enter into final stages with Liverpool, new bid set to be submitted. ??? #FCBayern #LFC are aware of his decision: Mané wants Bayern – and it’s really close now. pic.twitter.com/v8cDmrFS91
— Fabrizio Romano (@FabrizioRomano) June 15, 2022
Mane would be Bayern’s third signing this summer after Netherlands midfielder Ryan Gravenberch and Morocco right back Noussair Mazraoui were both signed from Ajax.