The Sun reports that United failed with their bid as the 20-year-old is keen to stay with Santos until after 2014 World Cup.
United made a move for Neymar after having been beaten by Paris St Germain in the chase for Lucas Moura.
United boss Sir Alex Ferguson could try with a new move for Neymar in the January transfer window.
Real Madrid and Barcelona have also been linked with a move for Neymar.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.