The former England captain is coming to the end of his deal at La Galaxy and is reported to favour a move back to the Premier League.
And after being linked with a loan spell for the midfielder, Beckham may make the move back to Tottenham, where he trained as a youngster before moving to Manchester United.
Harry Redknapp is known to be strapped for cash after Tottenham failed to qualify for the Champions League this season but signing Beckham on a free would represent a good piece of business for a player who was playing for AC Milan in the Champions League in 2010.
The move back to the Premier League would present an emotional dilemma for Beckham, who is a known United supporter, and made triumphant return to Old Trafford last month as part of Gary Neville's testimonial.
Beckham played 265 times and scored 62 goals for United during his 12 year career at the club.
As well as considering a deal from Tottenham, Beckham is also mulling over the possibility to being involved in Great Britain's football team for the 2012 Olympics.