Ajer is set to enter the final 12 months of his contract at Celtic and the club have agreed that he can leave if an offer that they deem appropriate arrives.
He has interest from the Bundesliga in the shape of Bayer Leverkusen, while Norwich and Newcastle in the Premier League are also keen.
Leverkusen and Norwich have both offered £10m for Ajer, but Celtic have rejected both proposals, leaving the player unhappy.
Ajer is clear that he wants to move on from Celtic this summer, however the centre-back is considering staying at the club and then leaving as a free agent next summer.
The centre-back would be able to sign a pre-contractual agreement with another club as soon as January.
As such the pressure may be on Celtic to recalibrate their expectations over a fee for selling Ajer, or they could risk losing him for nothing.
Norwich are keen to land a centre-back and boss Daniel Farke is now looking at other options in the event that Celtic do not change their stance on Ajer.
