Kansas coach David Beaty said both have recovered well and will be evaluated.
"Once you get that activity going, sometimes that tells you a little bit more about where they're at," Beaty said.
Beaty never said explicitly the two indeed sustained concussions. After Saturday's game, Beaty said Cozart had concussionlike symptoms. He didn't speak to Lee's situation until Tuesday.
Cozart was hit after attempting to throw deep to Steven Sims in the third quarter. Cozart was in the air after he released the ball.
"He got lit up," Beaty said. "It wasn't necessarily the hit, but his head hit the ground. . You could see his head hit the ground pretty good."
Redshirt freshman quarterback Carter Stanley took over for Cozart on the ensuing drive and finished the game.
Cozart, a redshirt junior, has played in seven games this season, totaling 1,075 yards passing, seven touchdowns and nine interceptions. He's shared starting duties with sophomore Ryan Willis.
The concussion protocol adds another layer to Cozart's tumultuous career.
In 2013, he started the last three games of the season as a true freshman, taking over for Jake Heaps, then a junior. As a sophomore, Cozart started the first five games but was relegated to the bench after coach Charlie Weis was fired. Michael Cummings became the starter.
Before the 2015 season, it was anticipated Cummings would start again, but a knee injury in Kansas' spring game ended his season. Cozart started the first two games of his junior year, then missed a start because of illness. He came back the following week to start against Iowa State but sprained a shoulder and missed the rest of the season.
Kansas hosts Iowa State on Saturday and is eyeing its first conference victory since 2014. The last time Kansas won a conference game, Kansas hosted Iowa State when Clint Bowen was interim head coach.