The teenage talent has starred this season in midfield for Reading, getting four goals and seven assists in 20 Championship games, particularly in December as Reading struggled for points, registering three goals and an assist in December before Christmas.
The 19-year-old is set to enter the final 18 months of his contract with the Royals, and discussions over a new contract at the club are yet to start.
According to Italian outlet seriebnews.com, Stefano Pioli's team are currently monitoring Olise's situation at Reading, after scouting him very well over the last few months, and are now lining up a switch.
The report adds that if Milan were to lure him to the San Siro, then it would be based on a 'long-term operation', wanting to loan him out to another Italian club, possibly a club in the low part of the Serie A table, or else one that is competing for promotion to the top-flight in the Serie B.
Some of the clubs being mentioned as potential loan destinations for the young Frenchman include Monza, SPAL, Lecce and Chievo Verona.
On the other hand, some of the Premier League clubs interested in him include Arsenal, Chelsea, Leicester City and Leeds United, whilst Tottenham Hotspur are also keeping a close eye on his progress in the Championship.