The 26-year-old Argentine centre-back is expected to cost the Premier League giants around £15million, after impressing for the Portuguese champions since joining from Real Madrid last year.
Red Devils boss Sir Alex Ferguson has had Garay watched several times already this campaign, most recently during Benfica's 3-1 victory over Sporting Lisbon on December 10.
A move to Old Trafford is being lined up at the end of 2012/13 as Manchester United seek a long-term replacement for Rio Ferdinand, who is in the final year of his contract.
Injury-prone captain Nemanja Vidic is also a cause of concern for Ferguson, with the Serbian stopper having managed just six games over the past year because of a recurring knee complaint.
Garay struggled to cement his place in Jose Mourinho's first-team during his two-year stay at the Santiago Bernabeu, but Real Madrid clearly felt the South American had strong potential, when they inserted a 50 per cent sell-on fee into the deal that took him to Portugal in 2011.
As a result, Benfica will demand a higher fee from Manchester United, who could also face competition from Serie A champions Juventus for the player's signature.