According to the Telegraph, who cite a report from Spanish publication Sport, the Red Devils made a £139 million attempt to sign the Brazilian.
The Blaugrana superstar was offered a staggering £280,000-a-week contract to move to Old Trafford - totaling £14.65m-a-year.
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The deal would have seen him become the highest earner at the Theatre of Dreams, ahead of captain Wayne Rooney.
In an exclusive interview with Sport, Neymar's father said: "United phoned Barcelona and got the answer that Neymar has a contract and is not for sale.
"Everyone is calm. Neymar still has three years on his deal. We are happy. Neymar chose to play here and he is super-happy in Barcelona."
The 23-year-old produced one of his best performances in a Barcelona shirt - to date - in their 5-2 dismantling of Rayo Vallecano.
In the absence of Lionel Messi, the South American scored four goals and was awarded two penalties as his pace and trickery proved too much for the opposition.
The thought of the former Santos man plying his trade in the Premier League is exciting, but it seems fans will have to wait some time for that dream to become a reality.
It may never happen. Neymar could quite feasibly spend the remainder of his playing days at the Camp Nou.
However, United fans should never give up hope. Anything can happen in football, just look at Angel di Maria. Although, that did not turn out well.
Will Neymar ever leave Barcelona? Have your say in the comments section below!