The Spaniard is currently on loan at the club from Everton – having signed for the Toffees in July 2015.
However, the Blaugrana have a buy back clause, that can see them buying the winger back to earn profit on the sale.
The 23-year-old is on Barca’s radar, with technical secretary Robert Fernandez has already stated that the club are monitoring his situation.
The Everton man joined the Rossoneri in January and has redeemed himself at the club, having scored twice in 11 appearances for the club.
The Diavolo have already informed the player that they will make everything they can to sign him on a permanent deal at the end of the season because they consider the player an important part of the club’s future under new ownership.
Milan general manager Adriano Galliani is keen to keep hold of the star to continue the progress made under Vincenzo Montella as the club look to make a return to European football after three-years.
“In June, you will know, I do not know what will happen in the market, so I cannot say anything,” Galliani told Milan TV.
“I have spoken with the people in charge of Barcelona, but I will not tell you what they told me.”
Deulofeu scored as Milan hammered Palermo 4-0 to move to sixth position in the Serie A table.