Sneijder is a Manchester United target but it is suggested the Premier League champions are unwilling to match the Dutchman's purported wage demands of around £200,000-a-week.
On Sunday, though, former Real Madrid playmaker Sneijder failed to completely rule out a move away from Inter this summer. However, Gasperini is unconcerned by the reports.
He told the club's official website: "The transfer market closes on August 31 and we have all been trained to live with these rumours for the duration of the season.
"I'm not worried or annoyed by these rumours and neither are the players. They are Inter players, they play their hearts out for Inter in any situation and they showed that today.
"People talk a lot about the transfer market but at the end of the day everything is just like it was at the start.
"Have Manchester United put in a bid for Sneijder? I don't know and I don't care, but it's not unusual for great players to be in greater demand.
"Inter's great players are, as are those from other clubs, but if you are sure that the player has received an offer, I'll remind you that Sneijder is under contract to Inter, so if there is a bid it should be made to Inter.
"I'll say it again: all too often rumours are spread for months and then, when it's all over everything is exactly as it used to be."