Reports emerged last week claiming that the Red Devils are ready to open talks with representatives of the Portugues giants over a move for the highly-rated 19-year-old.
However, Benfica released a statement denying such rumours and insisted that they have no interest in selling Neves to Man United or any other club.
Since the big-money departure of Enzo Fernandez to Chelsea in January last year, Neves has developed into a first-team regular under Benfica head coach Roger Schmidt and has become one of Europe's most sought-after midfielders.
Neves, who primarily operates as a deep-lying midfielder, has made a total of 50 senior appearances for the Eagles across all tournaments, including 26 starts so far this season, and he has been named Primeira Liga's Midfielder of the Month three times already since the start of the campaign.
Although Benfica have publicly expressed their desire to keep hold of Neves, the player's agent Jorge Mendes has suggested that a summer transfer could be on the cards for the midfielder as well as defender Antonio Silva, who has also been linked with Man United among a number of other top European clubs.
"Their (Benfica's) president Rui Costa will have to decide when he's ready to consider a deal," Mendes told Portuguese news outlet Record. "It's always the club's decision. I can take the proposals and the conditions."
Asked whether Benfica have received offers for either Neves or Silva since the January transfer window re-opened. Mendes said: "Yes, there have been situations in which any of them would have had offers if the door had been open.
"The players will stay at Benfica until the end of the season, that's for sure, and then Rui Costa will decide what's best to do. And then, as with all the other players: meetings, talks and, when the time is right, the decision will be made."
Benfica are under no pressure to part ways with Neves, whose contract at the Estadio da Luz runs until June 2028 and includes a €120m (£103m) release clause, while 20-year-old teammate Silva will see his deal expire a year earlier.
Speculation linking Man United with Neves, Silva and a host of other targets comes at a time when major changes at boardroom level are taking place at Old Trafford following the arrival of minority owner Sir Jim Ratcliffe.
The 71-year-old, who expects to have his 25% takeover of the Red Devils ratified by February, has been joined at the club by new CEO Omar Berrada, who was unveiled in his new role on Sunday after leaving rivals Manchester City.
While Berrada will begin work at Old Trafford at the end of the season, Ratcliffe is soon hoping to take charge of Man United's football operations and have a major influence in the club's transfer dealings.
The Red Devils are believed to be keen to make reinforcement in defence, midfield an attack, but it remains to be seen whether they will splash the cash during the January transfer window.