The 19-year-old is a huge prospect in European football and is wanted by many top teams.
Per Record in Portugal, United are among the clubs pushing to secure Neves in the summer.
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The likes of Liverpool, Chelsea, and Manchester City have all been linked to him this season.
Neves' Benfica teammate, Antonio Silva, is also of interest to the Red Devils.
However, Neves is the one they want to sign ahead of any other player, according to the Portuguese reports.