The Italian club have been keen to improve their right flank for some time now and according to Diario AS view the man from the Balearic Islands as the perfect option.
Milan want to begin negotiations to sign him in June, when he enters the final year of his contract at the Santiago Bernabeu.
Milan can afford his current salary of about €5m net per season but are aware that should a Premier League outfit come onto the scene they could be blown out of the water.
Paolo Maldini enjoys a fine relationship with Madrid and that should stand him in good stead. But everything will come down to Asensio himself and whether he sees it as a good move.
Asensio has scored ten goals in 34 games this season and has started 15 of Madrid’s 26 La Liga games. As Kylian Mbappe is expected to arrive in the summer this could be a good time to go.