Garay, who currently plays his football in Portugal for Benfica, was heavily linked with United throughout the summer window.
At various points reports claimed United had reached an agreement with Benfica for the transfer of the former-Real Madrid youth team player.
But a move never materialised and Barcelona are now plotting a move of their own in January as their hunt for a new centre-back continues.
FIFA agent Francois Gallardo told Spanish TV station Punto Pelota this week that Barcelona manager Tata Martino will prioritise the signing of a new defender in the winter window - with Garay at the top of his shopping list.
The Catalan giants have been linked with several centre-backs, including at least two from the Premier League.
But they were frustrated in their recruitment over the summer, and the report claims they'll resume their search at the earliest opportunity in January.
Garay, a 26-year-old Argentina international, spent time at Real Madrid before moving to Benfica in 2011.
He was linked with United over the summer but the reigning Premier League champions ultimately only made one big-money purchase - the signing of Marouane Fellaini from Everton.
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