The former Manchester United midfielder has been at the centre of speculation after failing to extend his contract with the MLS club, and he has denied that he is considering calling time on his career.
Beckham told BBC Sport: "People have been saying [I am too old] for the last 10 or 15 years and I've still continued to play for my country.
"Right now, I feel fit and still love playing, so I'm not finishing yet.
"It's always difficult making that decision about stopping but I don't think I'm going to have that problem. I think I'm going to know when to finish, but that's not yet.
"As long as I feel I can play at a high level, then I'll continue. Once that changes, I'm going to have to accept I need to stop."
The ex-England captain has been strongly linked with a move to Paris Saint-Germain, but says he has not considered his next move.
"At 36 years old, to still have that interest in me is an honour, I'm very flattered,” he added.
"But right now I'm a Galaxy player and I will continue to be a Galaxy player until we win the league - the MLS Cup - and then we'll see. I haven't even sat down and thought about what my options are yet.”
Since moving to America from Real Madrid in 2007, Beckham has been central in LA Galaxy’s side, and team-mate Landon Donavon spoke of his admiration of the Englishman, and hopes that he stays.
"We are all assuming that he is going to be back," Donovan said.
"I know nothing has been said, or nothing is official, but I think he loves it here, his family loves it here and he has been arguably our best player for long stretches during the season.
"He looks as good now as he did even five years ago when he first came here so I think we are under the assumption he is coming back and, if something changes, we have to adjust accordingly”
As well as being linked with PSG, QPR and Tottenham it has also been said that Beckham would like to buy a MLS side once he has finished his playing career.
"I have the option and it's something I probably will do," he explained. "Obviously I have to wait until I finish playing.
"I want to be part of something that is going to grow and I believe that this sport is going to grow."