The apparent approach came a fortnight before the transfer deadline passed in England, as United left it late before securing the services of Marouane Fellaini from Everton.
David Moyes turned to a man he knows well from his time spent in charge at Goodison Park after missing out on several other targets.
United were reported to be close to landing Athletic Bilbao's Ander Herrera, were said to have joined the chase for Mesut Ozil - who ended up at Arsenal - and failed with a big-money bid for Real Madrid's Sami Khedira.
Galatasaray have now claimed that the Red Devils also tried to lure Sneijder to the Premier League, with the Dutch playmaker having been regularly linked with a switch to Old Trafford for some years now.
The Turkish giants were, however, unwilling to discuss a deal, with it important for them to retain the services of key men.
Gala sporting director Bulent Tulun told Milliyet: "Sneijder received an indirect offer from Manchester United two weeks ago but it was not accepted.
"There are several clubs that want him but just like we can't let go of Burak (Yilmaz), we also have to keep hold of Sneijder."