United are reportedly making a move for the 24-year-old as a replacement for Zlatan Ibrahimovic, but Milan appear close to signing him, and are willing to pay €60 million.
His representative, Juanma Lopez, says the Spain international is keen to secure regular first-team football after struggling to dislodge Karim Benzema as the first choice striker in Madrid and will clear up his future in the near future.
"Alvaro is a player who wants to play a more important role," Morata's agent told Foot Mercato. "It makes sense for an attacker who has scored 20 goals. It's not enough.
"I do not know. It was a brilliant season for Real Madrid, they won so many titles. The player will make a clear and definitive decision in the next few days. I have not yet met the leaders of Real Madrid.
"[Milan's interest] existed and still exists, as for other major teams interested in a player of his calibre. He does not want to do a season like this again. It was a great season, but he wants to play more. We have not received any offers from France."
Morata returned to Madrid last summer after two years at Juventus and is contracted to the club until 2021.