Beckham injured the ankle in England's win against Estonia in June and could not train with the rest of the team at his first practice session Monday.
He did don the LA Galaxy kit however and worked with a personal trainer on stretches and recuperative exercises.
"We just want to get him on the field as quickly as possible but we don't want to put him in any danger of re-injuring it. It has responded though, in the last few days," Galaxy head coach Frank Yallop said.
"There is always a possibility that he won't play because of his injury but we're never going to force him to play. If he's ready to play, he'll play but we're waiting to see how he responds. We have to make sure we do the right thing by him."
Yallop added that he will err on the side of caution in playing his new star who was officially unveiled as an LA Galaxy player on Friday.
Yallop said Beckham's flight to Los Angeles from England on Thursday had not helped matters, and that the ankle had swollen because of the flight and possibly because Beckham had started running on it "maybe a little bit too soon."
The injury fear surfaced amid reports that Fabio Capello, Beckham's former coach at Real Madrid, has been offered a job to coach in the US in a further sign of the ambition that is taking hold of the game in a county where team sports are traditionally dominated by baseball, basketball and American football.
"They have contacted me," Capello told Gazzetta Dello Sport in Milan, without revealing who made the offer. "However, I must think about it.
"It would be a new experience that would intrigue me, not for the money but to see if anyone could make American soccer take off."
US football officials are hoping that the star power of Beckham and his Spice Girls wife Victoria Beckham will pull the sport into the mainstream.
But her debut on US television Monday night in an hour-long documentary called Victoria Beckham: Coming to America, was savagely reviewed by US critics.
The New York Post branded Victoria "relentlessly self-promoting" in a show described as "an orgy of self-indulgence" while the New York Times compared the programme to a website called cheddarvision.tv, where a webcam focuses on a piece of Cheddar round- the-clock, so cheese fans can watch the mould grow.
The St Louis Post-Dispatch summed up the challenge: "To the Brits they are Posh and Becks. To most Americans they are - who?" dpa
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