Cowboys owner and general manager Jerry Jones made the announcement Tuesday on his weekly radio show.
Lee has missed the last two games after pulling his left hamstring in the Cowboys' loss to the New Orleans Saints on Nov. 10. He had been expected to miss three or four weeks.
"I think I have a great shot for returning next week," Lee said after the Cowboys' victory against the Oakland Raiders on Thanksgiving. "I have to put the work in and go through practice and go through the progressions, but I feel great [and] I should have a good shot."The Cowboys (7-5) are tied with the Philadelphia Eagles for the lead in the NFC East.