According to the report, which cites his agent Curtis Stephens, Davis is expected to make a full recovery.
"He's going to fully recover and he's in good spirits," Stephens said. "Everything is being done on a precautionary basis. Two physicians both gave him a thumbs up. ... If camp opened tomorrow, he'd like to think he'd be there tomorrow."
This is the second time in the past three years that Davis has been shot.
He was an innocent bystander last time, and this time Davis was driving home from a family vacation.
Davis served as the Cowboys' starting free safety last season. This year, he's expected to compete with veteran Marcus Coleman and rookie Pat Watkins for the same spot.
He's also considered to be one of the top special teams players on the roster.