Despite making just 17 Premier League appearances for the Saints this season, the Uruguayan's representative Pablo Betancourt claimed that Ramirez could move to the San Siro at the end of the season.
"It would be a weighty inheritance to replace Kaka, but an honour for Gaston," he told The Mirror. "How could you say no to Milan, who are one of the best clubs in Europe?
"It would be an important opportunity for him. We are trying to understand which team can make the right offer to Saints.
"Ramirez played very well in Italy and many Serie A clubs remember him positively."
Ramirez was left out of the Southampton squad that lost 4-1 away to Manchester City on Saturday.