The 22-year-old has been linked with a move away from Celtic Park in the ongoing transfer window and Italian giants AC Milan are keen on the defender.
The Rossoneri are looking to add to their centre-back options before the transfer window closes and view the Celtic star as a candidate.
However, the Scottish champions are reluctant to entertain offers for the young defender, who Neil Lennon insisted the club are not willing to sell.
With the Bhoys not changing their stance on Ajer’s future at the club, AC Milan could be set to bow out of the chase for the centre-half, according to Italian outlet Calciomercato.com.
The transfer window has entered its final stage and AC Milan are willing to move on from Ajer and consider other options to bolster their defence as time is crucial.
The Norwegian has been in a key figure in Lennon’s defence and the Italians ending their interest in the player would be a huge boost for Celtic.
Ajer, who has two more years left on his contract with the Bhoys, is a key man at the back for Lennon.