Kinta, who suffered a strained left oblique in last week's loss at Arizona, didn't have a helmet and wore a sweatshirt with shorts as the Cowboys started practice.
Stephen McGee would get the start if Kitna is unable to play.
Interim coach Jason Garrett said the team is taking Kitna's status day by day and hasn't officially named McGee the starter for the regular-season finale at Philadelphia.
On Wednesday, Kitna said his oblique hasn't gotten better.
"I'm never pessimistic," he said Wednesday afternoon. "We're still a ways away from the game, so we'll just see. It's one of those things where it could be feeling really bad for three or four days and then the next day it could just be gone."