The Italian giants failed to strike a deal over the summer with the Hoops, however, the Norwegian remained on their wishlist ahead of the current January window.
The two clubs were involved in some business, though, with Diego Laxalt making the move to Glasgow on a season-long loan on deadline day.
Reports in recent weeks have suggested that it is now the left-back’s ‘priority’ to move to Celtic on a permanent basis, and there has also been a fresh update in regards to Milan’s interest in Ajer.
According to the reliable Corriere dello Sport, via Calciomercato.com, Milan are monitoring Ajer’s situation and could facilitate the inclusion of Laxalt in any negotiations.
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The Hoops may also wish to recieve some cash on top of Laxalt’s services, should they sell Ajer.