The Sun says Manchester United boss Alex Ferguson is a firm admirer of Sneijder's talents and was linked with a £29million bid for the playmaker last year.
Gasperini has hinted he could be prepared to offload the 27-year-old in a bid to raise funds for new recruits.
And the Inter boss cited the example of Zlatan Ibrahimovic — who was sold to Barcelona for £39m in 2009 and included Samuel Eto'o as part of the deal — as an example of how they have improved after selling a big-name player.
Gasperini said: "There is every intention on the club's part to come out of the transfer window stronger — not less so.
"But two years ago, Ibrahimovic left and the team was reinforced.
"All the players I have know how to play in many different roles. Last year, Sneijder also played in different positions."