But Gasperini, who replaced Leonardo at the San Siro in June, says that Sneijder will not be leaving in the near future.
"It's tough to say what Sneijder will do, but the club is doing everything it can to hold on to him," said Gasperini at his first press conference as Inter manager.
"I have no doubt that Sneijder is a great player.
"It's difficult to know what can happen in the next 50 days of the transfer market.
"Inter wants to become even stronger.
"Two years ago (Zlatan) Ibrahimovic left the club but the team was strengthened and became even stronger.
"Wesley's situation does not worry me.
"In recent years, Inter have made fewer mistakes in the transfer market than other clubs and have made the best choices. Hence, I can only be optimistic."