Before feeling ill, he was at Oaklawn Park in Hot Springs, Arkansas, for the Rebel Stakes, the website reported.
Earlier, “SportsCenter” reported Payton was the first known person in the NFL to test positive for the illness.
Payton said he did not go to the hospital, was not running a fever and did not have any respiratory issues, ESPN reported. He said he did not have a cough.
“I was fortunate to be in the minority, without the serious side effects that some have. I’m lucky,” Payton told ESPN. “Younger people feel like they can handle this, but they can be a carrier to someone who can’t handle it. So we all need to do our part. It’s important for every one of us to do our part.”