Lee confirmed later Tuesday afternoon that he's ready to return, saying he was "ready to roll" against the Bears and that he'll return to practice on Thursday.
Lee, who is second on the team with 93 total tackles, suffered a pulled left hamstring during Dallas' game against the New Orleans Saints on Nov. 10. He had been projected to miss three or four weeks, but he increased his rehab in an effort to rejoin the team sooner.
Jones confirmed on his twice-a-week radio show on KRLD-FM in Dallas that Lee, who leads the team with four interceptions, will return against Chicago.
"I think I have a great shot for returning next week," Lee said after the Cowboys' victory against the Oakland Raiders on Thanksgiving Day. "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 ranked 27th in the league in run defense and have allowed 13 rushing touchdowns, tied for eight most in the league.