The Argentine centre-back has long been linked with a switch to the Premier League, after attracting attention from a number of top sides on the back of his consistent displays in Lisbon.
It is now understood that scouts from both United and Chelsea were in the Portuguese capital on Thursday night to watch the South American during his Europa League clash with Tottenham.
The 27-year-old netted the opening goal of the 2-2 draw – which saw Benfica go through to the quarter-finals on aggregate – and was impressive throughout the 90 minutes.
United were linked with Garay last summer and although a deal failed to materialise, they have maintained an interest.
David Moyes is known to be looking to bolster his rearguard in the coming months, and may turn to the former Real Madrid man as he plans for life without Nemanja Vidic.
Chelsea are also keen on Garay ahead of what could be a busy off-season in West London.
Jose Mourinho has already agreed a deal for promising defender Kurt Zouma, but he is believed to be an admirer of the classy ball playing centre-back too.