The Benfica centre-back has been a long-term target for United. He was linked with the defending Premier League champions last season under Sir Alex Ferguson, and fresh reports had suggested David Moyes was ready to make a renewed effort in January.
But the Old Trafford club could face competition from Napoli. Benitez is keen to strengthen the club's defensive options, and has earmarked funds for a new centre-back signing.
The report claims several names are on his shortlist, including Liverpool duo Daniel Agger and Martin Skrtel and Benfica's Garay.
Napoli sporting director Riccardo Bigon is already sounding out Garay's interest in joining the Serie A club.
The 27-year-old defender is under contract with Benfica until the summer of 2015, but his current deal reportedly includes a €20m release clause.
Recent reports suggested the Argentina international was still on Moyes's radar, with United keen to back their new manager with funds in the January transfer window.