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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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