The 27-year-old was ruled out for the season in the Browns' win over the Buffalo Bills on Thursday and was replaced by former first-round Draft pick Brandon Weeden, who has struggled for consistency throughout his two years in the NFL.
Chudzinski told reporters: "We're looking at our options right now. We'll determine that.
"Obviously, we have two guys that are comfortable and that have been in the system. We'll just work through that. We have a number of different options that we can go."
The Browns are tied at the top of the AFC North with a 3-2 record.