Dodd played the first series of the second half in the 17-13 loss to North Carolina, missing on his two pass attempts while under duress.
During Sunday's conference call, Rutgers coach Greg Schiano said it may not be known for a few days whether Savage will be available.
"We're going to have to wait and see," Schiano said. "We're going to have some tests done early in the week. We'll have to wait a little bit to get a better reading, and we'll go from there. I really don't know from there.
"(Rib injuries) are really uncomfortable a lot of times. We'll see where that goes."
Dodd acknowledged he will spend a little more time studying the playbook and going over film this week to make sure he is ready if Savage cannot play.
"I'm going to approach it as I have been, just working hard and preparing and coming in and working hard at practice," Dodd said after the game. "Maybe (it will be) a little different, and just open everything (to study) a little bit, but as far as what I've been doing, I feel as if I've been pushing myself and preparing."
Savage was injured late in the first half when he was hit by linebacker Bruce Carter. He didn't come out of the Rutgers locker room until the second half was underway.
Dodd said he was uncertain if he would be going into the game to start the second half until he got out to the field.
"I was trying to get myself mentally ready for if I was going to go in," Dodd said. "I was making sure I knew what I had to do and be ready for any situation that could come up. I was getting mentally focused."
When Savage played as a true freshman last season, the playbook was trimmed to things he knew well.
"I'm comfortable with Chas," Schiano said. "Chas is a guy who's a real student of the game, has a good understanding. This is his second action in a real game. Unfortunately, he didn't get great protection when he tried to throw it and he got hit. Whatever he's called on to do, I think Chas will do a good job."
On Dodd's first pass attempt, he rolled left and threw the ball out-of-bounds because no one was open. On the second throw, Dodd was hit as he was trying to throw the ball down field.
"I think on the second one, there was a window that opened up, but I didn't feel the pressure coming," Dodd said. "On the first one, he wasn't open so I just threw it out (of bounds). Both plays kind of broke down a little bit."