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 32 million euros ($33.5 million) up front for Mané, with a further 6 million euros ($6.3 million) due when he meets a specified appearance clause and an additional 3 million euros ($3.15 million) based on individual and team achievements.
Mané just completed arguably the best season of his career, converting the clinching penalty in a shootout to win the African Cup of Nations for Senegal, helping his country qualify for the World Cup and being a star for Liverpool in a campaign when the club nearly achieved an unprecedented quadruple of major trophies.
His last game for Liverpool was the 1-0 loss to Real Madrid in the Champions League final last month.
He has won every major honor with Liverpool — the Champions League and World Club Cup in 2019, the Premier League in 2020 and both the FA Cup and League Cup in 2022 — and looks to be seeking a fresh challenge at the age of 30.
Mané has mostly played as a left winger for Liverpool but converted to a central striker for the second half of last season following the signing of Luis Diaz. He impressed in his new role, scoring nine goals in his last 14 games in all competitions.
Mané's arrival at Bayern would come amid uncertainty over the future of striker Robert Lewandowski, who said last month he wants to leave. Liverpool has already signed a replacement for Mané in Darwin Núñez.