A person familiar with the situation said on Friday that Liverpool have agreed a fee with the Bundesliga champions in a total package worth €41 million ($42.9m).
The person spoke to The Associated Press on condition of anonymity because he was not authorized to discuss details of the deal, which has not yet been completed.
Liverpool will receive €32m ($33.5m) up front for Mane, with a further €6m ($6.3m) due when he meets a specified appearance clause and an additional €3m ($3.15m) based on individual and team achievements.
Mane joined Liverpool from Southampton in 2016, arriving within the first 12 months of manager Jurgen Klopp's reign, and played a crucial role as the club returned to the top of English football -- he lifted the Champions League in 2019 and helped to end the club's 30-year wait for a Premier League title in 2020.
He also won the Club World Cup (2019), FA Cup (2022) and Carabao Cup (2022) as he scored 120 goals in 269 games in all competitions during his time at Liverpool.
There had been speculation throughout last season that Mohamed Salah could also leave this summer, but the forward confirmed last month that he will remain at Liverpool for the 2022-23 campaign.
Information from ESPN's Archie Rhind-Tutt and The Associated Press was included in this report.