The Uruguayan international has struggled to adapt to the Premier League since becoming the Saints club record signing in the summer of 2012.
The £12million signing from Bologna has found regular first team football hard to come by on the south coast, although he has shown glimpses of what he can do as a substitute under Mauricio Pochettino.
There has been talk to suggest Ramirez could be seen as the ideal replacement for AC Milan star Kaka, who is set to complete a move to the MLS at the end of the season.
Ramirez’s agent Pablo Betancourt said: “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?
“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 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.
“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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