"It's not a high ankle sprain. ... It was more of a typical sprain," Payton said, according to the Saints' official website. "It's looking a lot better. He's feeling a lot better. He's doing some light jogging, all those things. I think he's going to have a good shot at playing next week."
Thomas' absence means veteran Ladell Betts and rookie Chris Ivory will handle running back duties. Ivory showed flashes of brilliance in his first two NFL games, but he also lost two fumbles.
"I think the big thing with ball security on Wednesdays and Thursdays (in practice) is the emphasis of technique of getting used to it," said Payton, who added that Saints coaches teach their running backs to hold the ball high and tight to their rib cage. "It's different for guys growing up getting used to it.
"All the years he's played running back, he's probably used to a certain way of carrying the football. It's probably been OK. It's a bigger change. The way teams are taking the ball away now, it's obviously a bigger point of emphasis for anyone touching the ball."
Payton also confirmed that defensive end Will Smith (groin) and safety Roman Harper (hamstring) are questionable to play Sunday.
Tight end Jeremy Shockey (knee) is probable.
The Associated Press contributed to this report.