United made a £38m attempt to prise the 20-year-old from Santos, according to The Sun.
It was also reported that the move failed because Neymar had said he wanted to stay at the Brazilian club until after Brazil had hosted the World Cup in 2014.
However, United have immediately denied that a bid was made, and their denial was supported by Santos director of football Felipe Faro.
Faro told Globe Esporte: "I have no idea where it came from, but it is not true."
Despite being only 20, Neymar has already scored 113 goals in 190 games for Santos.