Ajer has been on AC Milan’s radar and the club’s scouts have thoroughly run the rule over him, compiling detailed reports on his strengths and weaknesses.
The Rossoneri want to bring in another centre-back and have been looking at Saint-Etienne’s Wesley Fofana, but a deal is claimed to be unlikely.
And, according to Italian outlet Calciomercato.com, the Italian giants are now once again on the path that leads to Ajer.
They explored a deal for Ajer in May and the club are working to provide the coach Stefano Pioli with a defensive reinforcement.
It is claimed that Ajer is valued at the €20m mark.
The centre-back is already into the thick of a new season with Celtic and has clocked seven appearances for the Bhoys in all competitions, also getting on the scoresheet against Ross County.
He has another two years left on his contract at Celtic Park.