The Sun says the club are ready to bid £15million for the Argentina centre-back at the end of the season.
United have watched Garay, 26, several times this term and have made their interest known to the Portuguese champions.
Alex Ferguson’s scouts studied him in the 3-1 win at Sporting Lisbon on December 10. And they were there again for Wednesday’s 2-1 away win at SC Olhanense.
But United will face a battle to get their man, with Italian champions Juventus also interested.