The Norwegian has established himself as a regular at the heart of the Hoops defence and his progress has caught the eye of several high-profile clubs including Real Madrid.
According to Todofichajes, the Rossoneri are said to have joined the pursuit of the centre-back and they have supposedly sent an emissary to negotiate a deal with the Scottish champions.
It is added that the San Siro outfit would ideally prefer to make a defensive addition on a free transfer (such as Paris Saint-Germain’s Thiago Silva) but they are tempted by the potential of Ajer.
The Rossoneri currently have five central defenders in Alessio Romagnoli, Mateo Musacchio, Leo Duarte, Simon Kjaer and Matteo Gabbia in the first-team squad.
Musacchio, however, has been fancied to head through the exit door while it is unclear whether the club will turn Kjaer’s loan deal from Sevilla into a permanent one.
As such, Stefano Pioli’s side may have to make at least one central defensive addition this summer, considering Duarte has barely settled at the club due to a long-term ankle injury.
While Ajer may appear an attractive option, the Rossoneri could face stiff competition from Leicester City, in particular, who are managed by ex-Celtic boss Brendan Rodgers.
Rodgers is credited with transforming the 22-year-old into a centre-back from a defensive midfielder and it remains to be seen whether there is a reunion on the cards.
Ajer has just over two years remaining on his Celtic contract. He has made 129 appearances for the Glasgow giants since his debut in 2016.
Stats from Transfermarkt.com