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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.