Witnesses confirmed the incident occurred in the garage at the site of Friday's Nationwide Dollar General 300 auto race at the Lowe's Motor Speedway in Concord, N.C., the newspaper said.
After a heated exchange of words, Harvick appeared to turn away from Edwards, who then reached for Harvick's shoulder, and Harvick responded by shoving Edwards, causing him to land on Harvick's No. 33 Chevrolet, witnesses said.
NASCAR officials said they considered the incident a non-issue, the newspaper reported.
Harvick and Edwards have been at odds since Edwards' car ignited a 12-car crash during last Sunday's Amp Energy 500 at the Talladega (Ala.) Superspeedway. The crash took place when Edwards bumped Greg Biffle from behind with 15 laps to go.
Harvick and Matt Kenseth were among the 12 drivers affected.
The crash led to a 12-minute caution.