The Italian international was quoted in an interview with Telenoche last week expressing his interest to play for Argentine outfit Boca Juniors in the future.
However, the former Roma forward has taken to Twitter to quell suggestions that he is already looking to leave the Saints, who he joined in the summer.
He tweeted: "I'm happy in the Premier League and I love Southampton !!! I do not understand why false things write..." [sic].
Osvaldo has scored just once since arriving at St Mary's Stadium.