The Argentine stopper was watched by United scouts last weekend, according to Spanish outlet Super Deporte, who claim Mourinho is determined to replace Phil Jones at centre-back.
Now 30, Garay has enjoyed an impressive career to date, playing at many of Europe’s top clubs including Real Madrid, Benfica and Zenit St Petersburg.
Last summer, Valencia shelled out €20m (£18.4m) to bring him to the Mestalla Stadium but a disappointing 16/17 campaign for Los Che could have opened the door for Garay’s potential exit.
Despite languishing in 12th in the table, Garay proved to be one of the team’s better performers.
He scored four league goals in 26 appearances – some of which are shown in the above clip – marking his most impressive tally since a stunning year with Benfica in 2013.
Garay also demonstrates his ability on the ball, acting a ball-playing centre-half while the team is in possession to help build attacks from the back.
But after years of links to the cultured defender, United fans reacted to news of the latest transfer rumour with some scepticism.
Gareth Bale – Real Madrid – 14/1 (BetStars)
“Ezequiel Garay will be retired and there will still be rumours #MUFC are trying to buy him. Every year,” said one fan.
Another wrote: “Probably nothing in it – but if there is, what does it say about Victor Lindelof?
“He’s a £30m signing and he can’t get on the pitch.”
It comes after reports emerged claiming Spurs left-back Danny Rose is set for crunch talks with chairman Daniel Levy amid news of a potential switch to Old Trafford.