United and Liverpool are both reported to be interested in signing the 19-year-old this summer.
Earlier this week it was claimed by DN Sports and O Jogo that the two arch-rivals were set toscrap it out for the Portugal international.
And A Bola now suggest United have an advantage in the race due to the presence of Mourinho.
They claim Neves is keen on a move to the Premier League, and in particular United now that Mourinho is in charge at Old Trafford.
Porto are ready to cash in on Neves as they are currently struggling to meet Financial Fair Play restrictions, according to DN Sports.
That report claimed Neves would be available for £17.1m but A Bola claim that it will take the full £34.3m of his release clause to strike a deal, which may prove to be a sticking point for United and Liverpool.
A Bola add that Porto are yet to receive any formal offers for Neves' services.