The Holland international was among the most sought-after talents in world football at that time, having inspired Inter to an historic Treble - which included a UEFA Champions League success.
United were in the market for creative talent and made an official approach, however, they were reluctant to meet Inter's asking price and Sneijder stayed on in Italy for another two-and-a-half years, before linking up with Galatasaray in January.
On United's interest in his services, the Dutch playmaker told Galatasaray Dergisi: "We had some talks with Alex Ferguson back in 2010.
"They [United] contacted the club after our Treble season but too much money was asked for. And I was also happy at Inter so I decided to stay.
"Manchester United are a fantastic club and they kept showing interest after that year but not as determined as before.
"I don't give much thought about proposed transfers, if I'm happy somewhere, I'm happy there."
Sneijder has also claimed that he had the opportunity to link up with Barcelona back in 2007, but opted to leave Ajax for their arch-rivals Real Madrid - a move which saw him fail to produce his best.
"Real Madrid were very persuasive about signing me," he added.
"There were two possibilities in Spain for me: either Real Madrid or Barcelona.
"Barca are really a great club and they have won everything for the past six years but I always liked Real Madrid's white shirt. I was very excited when they offered me a deal and took it immediately. And for me, they have a greater history than Barcelona."