According to ESPN, Palmer will back up Josh McCown, although could be given a shot as the starter if necessary.
Palmer was cut by the Bears after the preseason. He spent 2008-2010 as a backup to his older brother, Carson Palmer, when they were members of the Cincinnati Bengals. He had two stints with the Jaguars last year.
Cutler is expected is to miss four weeks with a pulled groin suffered Oct. 20 against Washington. The next day, it was reported Cutler could be ready to go sooner. Coach Marc Trestman, however, on Monday, told the Chicago Tribune he is not going to rush his quarterback's return.
“I don’t know that he’s trying to push it," Trestman said. "He wants to get back as soon as he can. That’s all I can really say, but I think we’ve got to stay in line with what the doctors have said, and if it’s better than that, we certainly would be happy about that.”
Cutler, who played stationary target for McCown Monday, is among at last two key players who will be on the sidelines when the Bears visit Green Bay Nov. 4.
Linebacker Lance Briggs is expected to miss five weeks with a broken bone in his shoulder while Charles Tillman is questionable with a injured knee.
In addition to signing Palmer, Chicago signed linebacker Larry Grant for insurance. Grant, a five-year veteran out of Ohio State, was with the 49ers in 2012.
The Bears (4-3) are in third place in the NFC North, behind Green Bay and Detroit.