Beckham made his first Major League Soccer start on Saturday, playing the full game as his the Galaxy lost 5-4 to the New York Red Bulls on the East Coast.
The Galaxy scored two in the space of five minutes early in the game - both Beckham assists - but lost to a last minute goal from former Aston Villa striker Juan Pablo Angel.
Beckham could be seen limping on his troublesome left ankle at times, and after the game he admitted he would have to wait and see if he would be fit this week.
"Only time will tell," he said. "I've got to see how it is tomorrow. It's swollen up at the moment but that was always going to happen. I'm traveling to London tomorrow morning to meet up with the team and hopefully I'll be playing some sort of role on Wednesday."
Beckham put in a full shift in the game with an early injury to Galaxy defender Ante Razic forcing a re-think from coach Frank Yallop on how to use his substitutions.
"I was surprised to actually play 90 minutes," Beckham said. "The manager and the coaching staff kept asking me if I wanted to come off. But I'm quite a stubborn person on and off the field. When we were winning I didn't want to come off and when we were losing I didn't want to come off.
"I think my stubborness took over and I didn't want to come off the pitch."
Beckham had initially been reluctant to play on the artificial turf used at Giants Stadium.
He added: "My ankle took a pounding obviously, I'm not used to this surface but it wasn't bad. There were a couple of instances where I rolled over on my ankle but at the end of the day we have to play on this surface. My ankle is more swollen than it was before the game but I'm sure it will be fine for Wednesday."
Yallop is clearly reluctant to let his star player go when he is obviously still battling the injury which has hampered his introduction to MLS.
Asked how he felt about releasing Beckham for international duty, Yallop took a careful line.
"It's a FIFA date, if the player is fit and he gets called up, he has to go," he said. "But he wants to go."
Asked directly if he wanted Beckham to go, Yallop simply repeated: "He wants to go."
Beckham sounded far more optimistic, and in his own mind he feels he could play on both Wednesday and Thursday, when the Galaxy face Los Angeles rivals Chivas USA in another MLS clash.
"I'm coming back (Wednesday night) and I'll be sleeping all the way on the plane, hopefully getting plenty of rest and able play some part of the Chivas game on Thursday. I think its important for me to get back and to be at the game. I'll definitely be there and hopefully I play some part in it."
To do that, he will have to convince Yallop he is not trying to do too much.
"I think David came through the game really well," Yallop said. "He was a little sore at the end. Whether he's ready to play on Thursday, to start the game against Chivas, is another thing.
"I guess we'll see what happens when he goes to the England squad and how much he plays in the game against Germany on Wednesday."
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