The veteran English midfielder is out of contract at the end of the current season and there is plenty of speculation about where he will continue his playing career in 2012.
"Right now I'm a Galaxy player, so that's all I can say," Beckham told reporters. "I'm enjoying myself.
"I want to win a trophy for this organisation. I think the way they treat the team, the way they treat the players and look after the players I think is the best in the league. So we owe them that."
And Beckham says that he is not taking too much interest in what is being written about him in regards to where his future lies.
"People have talked about my future for about 10 years. When I moved to Madrid in the first year, I think I was going to Chelsea about five or six times. So I've had that throughout my career," he added.