ESPN says United could be in the driving seat to sign Wolves star Neves because of Jose Mourinho's relationship with Jorge Mendes.
Manchester City have been linked with the Portugal international but now fear that the Red Devils could beat them to his signature.
However, Mourinho's close relationship with Neves' agent Mendes means United could now be at the front of the queue.
Mendes is also Mourinho's agent and is aware United would be interested if Neves becomes available.
But Wolves do not want to sell their star man and are believed to value him at close to £60m.