"We have to see how he (Barnett) comes off the wrist," McCarthy said. "Same thing with Chillar. That's his third shoulder surgery. You know how these things go. I'm glad we aren't playing this week. The season we had, I spent too much time with the doctors."
Barnett, a former starter, also has a steep price tag -- $6.9 million -- for next season.
Hawk signed a five-year, $33.75 million contract extension last week before the transaction deadline. Bishop received a reported four-year, $19 million extension in January.
"If he plays the way he did this year, there's no reason he shouldn't be (a three-down player)," McCarthy said of Hawk. "(Desmond) Bishop played very well, too. We line up tomorrow, it's A.J. and Bishop, and that's the way we finished."
Trading Barnett won't happen until a collective bargaining agreement is reached between the NFL and the NFL Players Association, Wyche reported, but the eight-year veteran could have value because there aren't that many quality inside or middle linebackers available in free agency.