A person with knowledge of the situation said on Friday that the Reds have agreed a fee with the German club.
The person spoke to The AP on condition of anonymity because he was not authorized to talk about the deal.
Up front, the Reds will get 32m, with a further 6m due and an additional 3m based on individual and team achievements.
In his first year at the club, he helped to end the club's 30-year wait for a premier league title by lifting the trophy.
The Club World Cup, FA Cup, and Carabao Cup were all won by him as he scored 120 goals in 269 games for the club.
There had been speculation last season that the forward could leave, but he confirmed last month that he will remain at the club for the next two decades.
This report contained information from The Associated Press and Archie Rhind-Tutt.
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