United scouts have watched the 18-year-old midfielder in action several times season and could make a move to sign the youngster in January.
The young midfielder recently became the youngster player to captain a Champions League side when he led the Portuguese side in their 2-0 win over Maccabi.
Ruben Neves has also been linked with the likes of Liverpool, Manchester City, Arsenal and Juventus.
Porto president Pinto da Costa recently insisted that Neves is not for sale.
Da Costa said: “Ruben has a contract until 2019 and not until 2017, as sometimes I see in reports.
“And we would like to keep him at FC Porto, as a kind of Joao Pinto. That is, he was a symbol and legend of the progress of the club for several generations.
“I never want him to leave Porto. Since I want him to stay for a long time he can be Porto’s greatest captain.”