The 22-year-old centre-back was on AC Milan’s shortlist of targets in the recent window and the club probed the possibility of signing him from the Scottish champions
Ajer was keen on the move, but Celtic were in no mood to sell him and it became clear that the Serie A giants would have to pay a big fee to snare him away from Parkhead.
The Rossoneri decided against spending big on Ajer, but he has continued to remain on their radar and the club are still interested.
And according to Italian daily Tuttosport, AC Milan could launch a fresh assault to sign the young centre-back as early as the January transfer window.
The Rossoneri management rate the defender highly and are keen to take him to Italy in the future.
A move in January could be on the cards but AC Milan could also wait until the summer to sign the Celtic star.
The Rossoneri management will get a closer look at Ajer when Celtic will host AC Milan in a Europa League group match on Thursday night.