The Uruguay international joined the Premier League club in a £12million deal from Bologna over the summer and has scored three goals in 18 top-flight appearances.
There has been speculation that Fiorentina and AC Milan were monitoring the playmaker's situation with a view to making a bid in the summer, but Pochettino is relaxed over the situation.
He told tuttomercatoweb.com: "Fiorentina and AC Milan interested in Ramirez? It's normal because Gaston is a young and strong player who is proving at Southampton he can rise to the occasion."
Pochettino has again confirmed that he was involved in talks to bring Philippe Coutinho to St Mary's from Inter Milan during the January transfer window, only to lose out on the winger to Liverpool.
He admitted: "I often spoken with him in the last weeks of January. I had him last year at Espanyol, I know him well. But eventually he went to Liverpool."
The former Espanyol boss, who was a surprise appointment to replace the sacked Nigel Adkins in January, also admitted he could take up a role in Italian football in the future.
He added: "Me on a Serie A bench? I like Italian football, I also have relatives in Italy. In the future, why not..."