The veteran safety, who had hip surgery in Colorado in April, told the NFL Network's "NFL AM" program Thursday that his rehabilitation is "going well."
"I know I'm probably ahead of schedule but at the same time I have to take it slow," he said.
Reed, 34, said he's usually running "full throttle" at this point of the offseason, but he's not at that point yet.
"It's definitely been a challenge but I'm always up for that, it's in my blood. I'm a challenger at heart," he said.
He credited the Texans for "standing behind me, understanding this process. And understanding that I'm doing everything possible to be at that first game."
He said the plan all along has been for him to be ready to play Week 1 when the Texans travel to San Diego to face the Chargers in the second game of a "Monday Night Football" doubleheader.
"I will be there that first game," he said. "I don't look for anything different unless me and the team, Coach [Gary] Kubiak decide to do things differently.
"And if we do that, it's about being smart. Because at the end of the day it's about being there in December and January and February when we make that trip to New York."
By New York, Reed was referring to the site of this season's Super Bowl -- MetLife Stadium in East Rutherford, N.J.
Reed signed a three-year contract with Houston this offseason after spending 11 seasons with the Baltimore Ravens. He was with his former team on Wednesday at the White House to help celebrate its Super Bowl victory.
"It was really awesome getting back and seeing my teammates," he said Thursday. "It was like closure because I hadn't seen them since I signed and I know they had a lot of questions and they were answered yesterday."