The 26-year-old Argentine international has been identified as a long-term replacement for Rio Ferdinand, and the Premier League leaders are believed to have offered £12.5million for his signature.
Red Devils boss Sir Alex Ferguson has twice sent scouts to run the rule over the former Real Madrid defender, and is keen to bring him to Old Trafford at the end of the season.
However, Benfica have told Manchester United they want £25million before they will even consider letting Garay leave Estadio da Luz.
The Portuguese outfit owe Real Madrid a percentage of any transfer fee, and will want to extract as much cash as possible.
According to Spanish newspaper, Marca, Garay would jump at the chance to join Manchester United, and an agreement between the two parties is thought to be the only stumbling block to the deal being completed.
Negotiations are unlikely to be finalised before the close of the January transfer window, but Ferguson will look to press ahead and secure the player's signature in the summer.