The 26-year-old was strongly linked with the Premier League champions earlier in the summer transfer window. However, the deal did not materialise as United were focusing on strengthening their midfield.
The report suggests that David Moyes is keen to add the former Real Madrid centre-back to his squad in January, as a future replacement for United veteran Rio Ferdinand. The former England international was offered a one-year extension in the summer but may not be offered another deal at the end of this season.
United scouts have been closely monitoring Garay at Benfica for the past few seasons. The Portuguese outfit will want around £20m for the defender while the Old Trafford club are likely to value the Argentine at around £15m.
Meanwhile, Moyes is also believed to be interested in Athletic Bilbao midfielder Ander Herrera and Porto star Eliaquim Mangala in a £68m deal in January. However, the former Everton manager has made signing Garay a top priority during the mid-season transfer window.
United have Phil Jones, Chris Smalling and Jonny Evans, along with the club's skipper Nemanja Vidic and Ferdinand, vying for positions in central defence. The addition of Garay to the Red Devils' squad in January would bolster their back four.
Any move from United will not be straightforward. The Express reports that Spanish champions Barcelona are also monitoring Garay and could provide competition for the centre-back.
Garay has two years left on his contract with the Portuguese club and is aware of the growing interest for his services. However, he earlier distanced himself from any move.
"I am under contract with Benfica and I am very happy here," Sky Sports quoted Garay as saying.
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