That’s according to German outlet Kicker, who claims Gerardo Seoane’s side are keen to bring in the Norweigan defender, who is understood to be valued at just £12.9m (€15m).
Ajer, 23, is expected to depart Celtic once this summer’s transfer window opens.
Seemingly unwilling to extend his contract, which expires next summer, the Hoops appear to be left with no choice but to sanction a transfer.
It has been noted that despite Bayer Leverkusen’s interest, talks between clubs have yet to take place, but that could all change in the coming weeks.
Bayer Leverkusen’s pursuit of the talented centre-back could be boosted though. The Germans and Celtic clearly have a strong relationship after Seoane recently recruited ex-Hoops right-back Jeremie Frimpong.