Herrera has spent the last three-and-a-half seasons at Old Trafford, scoring 16 goals in 151 appearances across all competitions.
However, the 28-year-old has been given a total of just 12 starts in the Premier League and Champions League this season and it has naturally led to speculation regarding his future.
According to Tuttosport, Milan are interested in giving the Spaniard a new start at San Siro as they look to put together a team capable of challenging for the top three in the Serie A standings.
Despite heavy investment last summer, Milan only sit in eighth place in the table, 27 points adrift of leaders Juventus.
Milan will allegedly send scouts to watch Herrera during the remaining months of the current campaign.