Cutler has been out of action for the past four games with an ankle problem and McCown has led the Bears to a 2-2 record in his absence, including throwing for four touchdowns in his side's win over the Dallas Cowboys on Monday.
"You want guys on your team that want to be on the field," he told the Chicago Sun-Times. "But also, you want guys on your team that know their roles and understand that.
"And so for me, I understand my role on this team. It's the backup quarterback. So, that being said, if Jay is healthy, he's ready to go. I'll support him and help him as much as I can."
The Bears are 7-6 going into their week 15 clash with the Cleveland Browns.