The Benfica defender is seen as the ideal replacement for Nemanja Vidic by Old Trafford officials and has been valued at 25 million pounds by his current club.
The 27-year-old defender, who is valued at 30 million euros by the Portuguese giant, has been subject to preliminary talks between both clubs in recent days with United keen to continue negotiations this week.
United considers the Argentine as an ideal replacement for Nemanja Vidic, who will almost certainly leave Old Trafford in the coming months alongside Rio Ferdinand.
Vidic, who earns 110k pounds per week at Old Trafford, is wanted by Galatasaray this summer but could leave in the January transfer window if United can secure a deal for the Benfica star.
Garay has not been considered a top target for Moyes this term but the United manager has been forced to widen his transfer search ahead of the January window, with the Scot’s ideal shortlist cup-tied in the Champions League and unavailable.
Moyes recognizes that his defense needs a significant overhaul, with Vidic, Ferdinand and Patrice Evra all likely to move on from the Premier League champions come the end of the season.
The former Everton boss was spotted scouting Cagliari defender Davide Astori and Juventus midfielder Claudio Marchisio on Sunday, while coach Phil Neville visited Spain to cast his eye over Rayo Vallecano's 19-year-old defender Saul Niguez, on loan from Atletico Madrid.