The Benfica defender has been heavily linked with both United and Zenit, and reports in the Russian media this week had claimed Zenit had won the race for his signature.
The deal reportedly agreed to bring Garay to Zenit was thought to be worth €14m with the Argentine international set to earn €6m-a-season.
But A Bola reports that Benfica will not let Garay leave before the close of the Russian transfer window - it shuts at midnight on the 27th February.
The Portuguese giants currently sit first in the Liga Sagres table, five points clear of Sporting and seven points clear of rivals Porto.
Benfica coach Jorge Jesus does not want to lose Garay, an important part of his side's miserly defence, with a league title still up for grabs. But he may be available this summer.
That's good news for United, who are thought to be targeting Garay as a long-term replacement for departing club captain Nemanja Vidic.
The Serbian international has already confirmed that he will leave Old Trafford at the end of the season, with Inter Milan thought to be interested.