New reports claim Van Gaal has shown interest in signing the attacking midfielder following the news he could leave Champions League outfit Galatasaray this summer.
Chelsea are also understood to be interested in the the 29-year-old, who managed 12 goals in 28 games in the Turkish league.
Gala bosses have made it clear they expect any club interested in signing Sneijder to cough up at least £12.5m for the former Real Madrid ace, who they signed from Inter Milan for £6m in January 2013.
Speaking last month, Galatasaray president Unal Aysal said: “If Chelsea were to offer a deal worth over €15 million (£12.5m) I would give Sneijder permission to leave if that’s what he wanted.”
The reports add that Sneijder has made it clear he isn’t open to a return to Italy and would be more willing to leave the Turkish outfit for a top English club.
It follows the news that Marouane Fellaini could be set to leave United after less than a year at the club.
United top brass are willing to let flop Fellaini go if they find someone willing to splash out £15m to buy him.