The 26-year-old centre-back has been identified by the Premier League champions as their primary defensive target this summer, amid growing concerns over the long-term fitness of both Rio Ferdinand and Nemanja Vidic.
New Red Devils boss David Moyes is keen to recruit a high-quality back-up for last season's first choice pairing, and believes the Argentina international is the man for the job at Old Trafford.
With a £17million valuation, Garay won't come cheaply, and it's hoped he will go on to establish himself in the Manchester United first-team in the future.
His arrival will provide a fresh injection of impetus in the 2013/14 campaign, whilst also providing competition for the likes of Jonny Evans, Phil Jones and Chris Smalling at the heart of United's defence.
Garay has impressed during his two seasons in Portugal, after arriving at Estadio da Luz from Real Madrid for a €5.5million fee in the summer of 2011.
The South American stopper signed a four-year deal with Benfica, with his former club retaining 50 per cent of any sell-on fee, should the Primeira Liga side sell to Manchester United this summer.