The 22-year-old central defender was heavily linked with a move to AC Milan in the recent transfer window and the Rossoneri explored taking him to the San Siro.
However, with Scottish Premiership champions Celtic keen to keep hold of their star defender, Ajer ended up staying put at Parkhead beyond the window.
The Rossoneri have not given up hope of signing the Norway international despite failing to do so in the summer and are said to be still keeping track of Ajer.
AC Milan got a first-hand look of Ajer when they took on Celtic in the Europa League on Thursday and were impressed with what they saw, according to Italian daily Corriere della Sera.
Stefano Pioli’s men returned from Scotland with a 3-1 win over the Hoops, but were convinced of what Ajer could bring to the table.
Rossoneri sporting director Frederic Massara and technical director Paolo Maldini, a former defender himself, watched the centre-half in action and were happy with what they saw.
AC Milan could be now in line to make another attempt to snap him up from Celtic in January, with the club willing to offer as much as €25m for the star.