A fee which the PA news agency understands to be £65million was agreed on Sunday after the Bundesliga champions returned with an offer closer to what the Anfield club consider the market value for the 28-year-old.
Diaz was given permission to leave the Premier League champions and on Monday he departed Tokyo, where the team are preparing for Wednesday’s match against Yokohama F Marinos, for Germany.
The player had been pushing for a move since last summer and, after two failed attempts to agree an extension to the two years he had remaining on his contract, Liverpool reluctantly accepted his departure was inevitable.
Hugo Ekitike’s arrival last week means the Reds have already bolstered their attacking options and they maintain an interest in Newcastle’s wantaway striker Alexander Isak.