Beckham has been sidelined since March when he suffered an Achilles tendon injury, while playing on loan for AC Milan, that cost him a place in the England squad at the World Cup in South Africa.
"The doctors' original date was October 1 but I always kind of said I want to be ready before then," he told the team's website.
"I'll keep my fingers crossed and hopefully will play in part of the game here against Columbus. I'll be on the bench, and hopefully I'll get on the field for 15-20 minutes. That's what I'm looking at."
Beckham took part in his first full training session with the club on August 11 and said he has had ups and downs.
"At the moment, you have good days and you have bad days. You wake up with a lot more pain in your body when you're in preseason. I have to do it because I need to get as close to match fitness as possible," he said.
"It's a bit difficult because when you don't play in games; that's where you get the real fitness from. But I'm doing what I can in the gym and what I can on the field, just trying to get strength back in my leg.
"It kind of kicks you up the backside when you realise you can't do certain things. Working out was something I've done for the last 25 years, and to not being able to do it was tough for me."
The former Manchester United and Real Madrid midfielder said he was still tentative in some areas of movement.
"When you do go through a trauma like this, an injury like this, there's always going to be that thing in the back of your mind saying, 'The last time I did that motion was when it actually snapped'. Cutting and turning and pushing off is still difficult for me, but that's going to come in time," he said.
The 35-year-old Beckham said he had never considered retirement and added that he had been grumpy at home.
"It's probably better asking my wife that more than me. Being around the house, not being able to train, not being able to play, I think it's been worse for her than me. It's been a long road," he said.
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