Although Beckham played for 12 minutes in his much-hyped Galaxy debut against Chelsea on Saturday, Yallop said the England midfielder needed more time to recover.
"He didn't train today and he is doubtful for tomorrow," Yallop told a news conference in Hollywood on Monday to launch the inaugural SuperLiga competition.
"He's getting normal ice treatment and a lot of massage to try and get the swelling down. His ankle is still a little bit tight, although it has improved over the last week. But he needs to get to a point where he's comfortable.
"We will have another look in the morning and, if it looks really good, then you never know. He might come on toward the end. But realistically we will probably wait until the weekend."
The Galaxy are scheduled to host Pachuca at the Home Depot Center on Tuesday in their opening SuperLiga match before taking on Mexican club Guadalajara at the Los Angeles Coliseum on Saturday.
The SuperLiga, which offers $1 million to the inaugural champions, is an eight-team competition featuring four Major League Soccer sides from the U.S. and four teams from the Mexican first division.
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Beckham, one of the most recognisable players in the game, would be a headline attraction in the SuperLiga but the Galaxy have the longer-term
"We want to make sure David is 100 percent," Galaxy president and general manager Alexi Lalas said . "We have games next week, next month and over the next five years. Everyone will get their chance to see David Beckham."
Beckham, signed by the Galaxy from Real Madrid on a $32.5 million five-year deal, gave his new team a brief scare on Saturday when he took a tumble late in the match as he tried to evade a tackle from Chelsea's Steve Sidwell.
Asked what went through his mind as he watched the former England captain lying motionless on the ground, Yallop replied: "Everything really.
"David is a competitor and he wanted to be out there and be a part of the action. But there was no malice by the Chelsea player and it was actually his other ankle."
Yallop said he had no regrets over Beckham making a brief cameo appearance against the FA Cup holders, despite playing with a heavily strapped ankle.
"It didn't make it any worse and that was important," he said. "Between all of us, we made a decision that we would do that, although the tackle was a bit of a worry when he was down. But he's fine and hasn't gone backwards."