The pair had been tipped by the Daily Mirror to join forces in charge of the national team once Fabio Capello's reign is over.
Spurs boss Redknapp is keen to bring the former England captain on a short-term loan from Los Angeles Galaxy - and it was suggested that may be just the start of their working relationship.
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But in a short statement, an FA spokesman said: 'There are no such talks and we have not discussed any potential succession plan with anyone at this point.'
Beckham is potentially available to Spurs until March having made similar moves to AC Milan in the past two MLS off-seasons.
Speaking after the defeat at Everton, Redknapp admitted he is keen to seal the deal: 'I will speak to the chairman and see where we are at. It is definitely not done - one million percent not. I don't know what has happened.
'I have left it to the chairman to deal with. I think we could do with his know-how, I think he has something to offer but it is out of my hands. I've said I'd like him but it is up to others now whether there is a deal to be done.'
Beckham nears Tottenham switch after LA Galaxy's green light to loanWest Ham set to sack Avram Grant in Premier League bloodbath with Roy Hodgson, Carlo Ancelotti and Gerard Houllier all on the brink
Explore more:People: David Beckham, Fabio Capello, Harry Redknapp Places: United Kingdom
Source: Daily Mail
Source: Daily Mail