The New Orleans Times Picayune reported that an MRI done Tuesday revealed no structural damage to the ankle.
Rivers did not return after he landed awkwardly on a layup attempt in the second quarter of the Hornets' 87-74 loss to the Mavs.
Rivers was selected 10th overall in the draft and is the son of Boston Celtics coach Doc Rivers. The Hornets hope the younger Rivers can pair with fellow rookie, and No. 1 overall pick, Anthony Davis to form a formidable core for the future.
Earlier Tuesday, Austin Rivers had been seen at the team's practice facility wearing a walking boot, the newspaper reported.
"It's actually not that bad,'' Rivers said after Tuesday's practice. "This is not really swollen. But it's not too bad just based on how I feel right now. I can be back very quickly. I'm not really worried about it."
Despite his own diagnosis of the situation, the paper reported that Rivers will likely be held out of the Hornets' remaining preseason games.
Rivers hurt his right ankle while playing in the Las Vegas summer league, that injury required arthroscopic surgery to get rid of bone chips.
"This has nothing to do with my surgery," Rivers said. "It was a bone spur, they scoped it and it's 100 percent now. This is completely different; I really landed awkwardly.
"My body fell on top of my ankle; I never landed like that before. It's just one of those freak things that happened. I'm hoping it's just some minor little sprain or something or maybe some (loose) cartilage, a bruise. I'll be back very soon."
The Hornets open the regular season Oct. 31 at home against the San Antonio Spurs.
Information from The Associated Press was used in this report.