The 31-year-old is out of contract at the end of the season and has also been linked with Spanish side Valencia, but a move to the San Siro may not be far away.
Tuttomercatoweb reports that the French international is impressed with Nerazzurri president Erick Thohir’s proposal and is willing to say yes.
However, the former Lyon man has not yet confirmed that he will leave the principality and the club remain hopeful of extending his current contract to keep him at the club.
“Jeremy is essential for our team,” Monaco vice-president Vadim Vasilyev told Caughtoffside.com.
“We have launched negotiations with his agent to prolong his contract for more than one year.”
Toulalan has made 36 appearances in all competitions for Les Rouges et Blancs this season, after joining from Malaga in 2013.