Beckham was ruled out of the current back-to-back clashes with Estonia and Russia with knee and ankle problems.
Galaxy, with just two games left of the regular season, can still make the end of season play-offs.
And that will give Becks more opportunities to convince England boss Steve McClaren of his match-fitness ahead of Croatia's visit to Wembley on November 21.
If Galaxy medical staff give the green light, the midfielder will face New York Red Bulls in California on Thursday ahead of the potential winner-takes-all play-off decider with Chicago Fire next Sunday.
And Becks said: "I can sprint and run and I now I just need to work on striking and passing the ball a bit more."