Speaking at the Soccerex Global Convention in Manchester, Neville said:
'I think he could achieve anything he wants to achieve.
'You could see him going up to government level or to head the FA or to do something in America that is not just average - he doesn't do anything that is average.
'He wants to do something that is going to leave a legacy, a stamp.
'I heard him talk this week about being involved in the FA.
'It would be silly of the FA not to take up that kind of offer, because what an unbelievable ambassador he is.'
Beckham has played 115 games for the English National team and also is a celebrated ambassador for the beautiful game world wide.