The 32-year-old England midfielder, sidelined since late August after spraining a ligament in his right knee, began light training with the Major League Soccer (MLS) team last week.
"The good news is that he is training and doing everything that all the other players are doing," Lalas told Reuters in a telephone interview on Thursday.
"We are still assessing not just his training but his recovery from the training because it's been a while since he's done this.
"I doubt he will play a role in the game this weekend but we will certainly look to have him play a part in the game on Thursday, if he continues to train and things go well."
The Galaxy, who languish in fifth place out of six clubs in the Western Division of the MLS, host Toronto on Saturday before taking on New York Red Bulls five days later.
Beckham's new team end their regular season campaign against Chicago Fire on October 21 and need to win all three games to advance into the playoffs.
Despite making a dismal start to the year, the Galaxy have kept their faint playoff hopes alive with a run of four wins in their last four MLS encounters.
"It's been exciting, not just for us but for our fans despite what has been a uniquely challenging year to find a way to still be in the running for the playoffs and to have control of that for the next three games," Lalas said.
"It's wonderful but it shouldn't mask what has so far been a sub-par year."
Asked whether he regretted playing an injured Beckham too soon, Lalas replied: "No. I say that with the understanding that we are living in anything but an ideal climate when it comes to the evolution of soccer in the United States.
"Ideally, if he were to come here in July and recognising that he wasn't 100 percent, we would have shut him down for the month and not played him at all."
Former England captain Beckham joined the Galaxy in July on a five-year contract which could potentially earn him a reported $250 million (123 million pounds), mainly from endorsements.
However, he played only 310 minutes in six games for his new team because of a nagging ankle injury before spraining his knee on August 29.
Although Beckham's sporadic appearances represent a poor return on his annual salary of $6.5 million, he has already provided a significant boost in interest that the MLS was convinced he would bring to soccer in the U.S.
Merchandising sales have risen dramatically, the profile of the game in the media has been enhanced and traffic to MLS's official website has doubled.
"People have to understand that we are an emerging soccer nation and we were given an opportunity that we had to take advantage of for the good of the game," Lalas added.
"And David Beckham recognises his responsibilities, not just for the Galaxy but for the good of the MLS and soccer in the U.S. It's easy to look back and second-guess but, with the perspective of where we are going, I think we made the right decision."
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