Hinrich, who missed Saturday's game against the Toronto Raptors, did not go through Monday's shootaround.
"He's feeling a little better," Thibodeau had said after the shootaround. "But he didn't do anything this morning, so we'll see where he is tonight."
Teague started in Hinrich's place Saturday, scoring seven points in 28 minutes. Augustin is 1 for 10 from the field in his first two games as a Bull after signing as a free agent last week.
"Some good, some bad," Thibodeau said of watching both point guards on tape over the weekend. "I thought we still had a shot in that game [on Saturday]. It was four [points] with 10 minutes to go. And then we struggled down the stretch. D.J. was limited because he had a very small package to work with and that sort of got us away from some of the things that we had been doing well with the second group.
"So I think we're a little bit more comfortable now with that. I thought Marquis, I thought his defense was very good, and I thought he attacked the basket well. So he's got to build off of that."