Osvaldo made the move to St Mary's from Roma in the summer and has helped Saints make a stunning start to the season, with Sunday's 2-0 victory over Swansea City propelling them into fourth place.
He was quoted in an interview with Telenoche last week as saying that he would be interested in playing for Boca Juniors at some point in the future, whilst also noting how the Premier League was more physical than the Spanish or Italian game.
But Osvaldo has now taken to Twitter to make it clear that he is enjoying English football and is feeling good at Southampton.
He wrote: "I'm happy in the Premier League and I love Southampton !!! I do not understand why false things write..." [sic].
Osvaldo, who has scored one goal so far for Southampton, was taken off early in the second half against Swansea due to a minor knock.
Mauricio Pochettino says he will be fit for international duty after being selected in the Italy squad for their final two World Cup qualifiers.
I'm happy in the premier league and i Love Southampton !!! I do not understand why false things write...- Dani Osvaldo (@danistone25) October 7, 2013