Led by sporting director Hasan Salihamidzic, Bayern representatives had face-to-face talks with their Anfield counterparts and appear to finally have got a deal for the 30-year-old over the line.
After bids of £25m and £30m were rejected by the Reds, a third proposal has satisfied all parties and it is thought the contract will keep him in Munich until 2025.
Mane has one year left on his Liverpool deal and made it clear after the Champions League final that he wishes to move on after six years at the club.
He joined Liverpool from Southampton in 2016 for £35m, scoring 120 goals in 269 games for the club.
Mane has picked up a host of trophies during his time at Anfield including the Champions League, Premier League, FA Cup, EFL Cup and FIFA Club World Cup.
He has formed a formidable attacking partnership with Mohamed Salah and Roberto Firmino during his six years on Merseyside.
Liverpool confimed the signing of Benfica striker Darwin Nunez erlier this week for £85m as they prepare for Mane's exit.
The Reds also signed Luis Diaz in January so will continue to boast a formidable attack even without Mane.
In addition to Mane, Takumi Minamino is also expected to leave Anfield with Monaco and Lyon interested, with Divock Origi already having already departed.