The Red Devils are said to be serious about bringing in the defensive midfielder.
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Neves may be seen by United as the long-term successor to Brazilian midfielder Casemiro.
The veteran is being linked with a move to the Saudi Pro League this summer.
Per Portuguese sources, United have already put in a first bid for Neves, which has been rejected.
Benfica are not eager to sell and will hold out for an extreme sum to get a deal done.