Garay was consistently linked with United and Paris Saint-Germain last summer, but the Argentine defender was still at Benfica when the transfer window closed.
The 27-year-old has revealed that previous United boss Sir Alex Ferguson showed interest in his signature, but believes that Moyes pulled the plug on the potential deal, deciding that he did not want to meet Benfica's asking price.
He is quoted by The Mirror as saying: "I believed I was going to join Manchester United in the summer. The deal was nearly closed but finally Benfica did not accept the offer.
"I believe the exit of Ferguson has influenced the deal. Moyes did not believe in me as much but that's not a problem.
"I am happy at Benfica and have a lot of dreams and ambitions for this season. Now I only think about the present which is Benfica but it's never possible to discard anything in the future."
Former club Real Madrid are due a significant chunk of any transfer fee Garay accumulates for Benfica, with Barcelona joining United on the list of clubs believed to be monitoring his progress.