TalkSPORT says United are keen on securing a deal for Neves, who has thrived in the midlands since joining from Porto back in 2017.
Arsenal retain an interest in the 24-year-old but United are now ahead of the Gunners in pursuit of the central midfielder.
Neves is represented by Jorge Mendes and has been in talks with Arsenal over a move in recent weeks.
Neves has two years remaining on his contract and would cost in the region of £35million for his suitors.
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