Ramirez, 23, is shaping as a transfer target for Milan, and would be the ideal replacement for Brazilian Kaka - who looks set to depart Italy for the MLS at season's end.
Ramirez's agent Pablo Betancourt said the San Siro club had inquired about securing his services, as he has helped the south England club into a likely top-10 finish in the Premier League this term.
The left-footed playmaker has made 43 league appearances for Southampton, since switching there from Serie A outfit Bologna.
"It would be a weighty inheritance to replace Kaka, but an honour for Gaston. How could you say no to Milan, who are one of the best clubs in Europe?" Betancourt said.
"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 has been underused by manager Mauricio Pochettino this season, playing just 17 league matches of a possible 33.
And Betancourt said his lack of game time had forced Ramirez to look for another suitor.
"Ramirez was very happy in Serie A and would be content to come back to Italy, but first any club needs to reach an agreement with Southampton," the agent said.
"Has it been a season to forget? Absolutely yes. He hardly ever plays, yet two summers ago the club made an important investment to buy him.
"Today you cannot say he's important for Southampton, seeing as he always starts from the bench."
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