It has been widely speculated that Sneijder could be set for a move to Manchester United as a long-term replacement for Paul Scholes.
Spanish club side Malaga are also believed to have lodged a significant offer for the Dutchman, thought to be in the region of £30 million.
However, Gasperini believes that his star player’s future lies at the San Siro.
"Sneijder is here and he wants to stay. The approach [to pre-season] has been very positive," the 53-year-old told La Gazzetta dello Sport.
And Sneijder himself has reiterated his desire to stay put, despite the reported interest of the Red Devils, although he did not completely rule out the possibility of him leaving Inter.
''I would like to remain. I have marvellous team-mates," he said in the July issue of Vanity Fair magazine.
''[Inter captain Javier] Zanetti has an extraordinary character, he has kept us together even at times when the morale was low.
''My wife Yolanthe and I love Inter, the Italian fans and Italy.
''Of course, if the club decided to sell me, I will go wherever they tell me to go. But I would be disappointed. We have felt so good here that I would miss the city of Milan and Inter.
''But football is like that. When I was sold from Real Madrid to Inter, I would have preferred to have remained in Spain. Whatever will be, will be.''
