The defensive end underwent a knee procedure in July, which prevented him from taking part in the team's training camp, five pre-season games and regular season opener against the New York Giants.
The 29-year-old told the team's website: "I feel good. We'll see how it feels in the morning. But everything I've been doing has been getting better every day, I haven't had any setbacks. If everything keeps going the way it's going I should be back sometime soon.
"I'm just going to play it by ear, see how many plays I got today, try to add a little bit more tomorrow, add a little bit more Friday leading to the game.
"It's probably going to be a couple of games [until I am fully fit]. I do a lot of those conditioning things on my own, so I try to get that under control as best as possible. But it's probably going to be a little bit."
Spencer made 55 tackles, 11 sacks and two forced fumbles for the Cowboys last season.