
The England midfielder confirmed his return to AC Milan on loan this week as he tries to secure a place in Fabio Capello's World Cup squad.
Beckham, 34, was tipped to quit his £25million-a- year deal with the Galaxy long before it expires at the end of 2011.
But the former Three Lions skipper now says he could be persuaded to agree a new contract in LA that would take him close to his 40th birthday.
He said: "There is every chance that could happen. I signed a five-year deal and I always said I would honour that.
"I am good friends with the owner Tim Leiweke and everybody else at AEG. They have been great to me in the support they have shown. We will see what happens."
Becks will return to America after the World Cup and play out the rest of his lucrative deal.
Galaxy failed to make the play-offs in his first two seasons. And he also fell out with team-mate Landon Donovan over his comments in a book The Beckham Experiment, which told of the problems experienced by the franchise.
But the Galaxy are now just three wins away from winning the MLS title.
And they face rivals Chivas USA in today's play-off second leg at the Home Depot Center.
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