Kosier said there is no damage in the knee, which is the same one he injured during training camp, forcing him to miss the season opener. Someone fell on Kosier's leg, and he came out of Sunday's game early.
Witten continued to play in the game after being hurt.
Before Phillips spoke, the Fort Worth Star-Telegram reported that Kosier was expected to miss up to four weeks because of the injury.
The Associated Press contributed to this report.