Sir Alex Ferguson Former Old Trafford boss had been monitoring the Argentina international and the 27-year-old claims a deal was almost completed before the Scot retired.
Garay believes Moyes baulked at the price tag with Benfica having to pay his former club Real Madrid a slice of any transfer fee.
‘I believed I was going to join Manchester United in the summer,’ he said. ‘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.’
Barcelona are also interested in Garay as they seek a long-term replacement for veteran Carlos Puyol.
He joined Real Madrid from Racing Santander in 2008 but could’nt hold down a first-team place at the Bernabeu.
Garay joined Benfica two years ago and has won 11 caps for his national side.