According to Sky, the 19-year-old is set to move to the BayArena for a fee of €2m plus add-ons, with Erlein still under contract at Hoffenheim until 2029. Eintracht Frankfurt had also shown interest in the defender last winter, but Leverkusen have moved decisively to get the deal done this summer.
Erlein is expected to sign a contract through to 2031 once the move is finalised.
The transfer follows Bayer Leverkusen's recent business with Afonso Moreira, 21, and 16-year-old Kennet Eichhorn, both of whom arrived at the club earlier this summer as part of the same recruitment push. Unlike that pair, however, Erlein is not being lined up for an immediate role in Leverkusen's first team.
Instead, the Germany U19 European Championship runner-up is set to be loaned straight to 2. Bundesliga for the coming season to continue his development at a higher level of senior football.
Erlein made his mark for Hoffenheim's reserve side in the third tier last season but has not yet had a senior taste of first-team football at the Rhein-Neckar-Arena, with his only involvement in the matchday squad coming in the second round of the DFB-Pokal against St Pauli, which Hoffenheim lost 9-10 on penalties.
The move is notable given Hoffenheim only extended Erlein's contract early this year, with the club describing the young right-back as an important building block for their future at the time.
The plan at Leverkusen is to build him up carefully rather than throw him straight into senior football at the highest level, with a loan club for next season yet to be confirmed.
Erlein has also broken into Germany's youth international set-up, representing the country at various age groups on his way to that U19 European Championship final appearance, and is regarded as one of the more promising defensive prospects to emerge from Hoffenheim's academy in recent years.