Jones (triceps) was placed on injured reserve Wednesday.
Jones exited Sunday's game against the Lions with a triceps injury and will not return.
Jones is slated to sign a three-year, $30.1 million deal with the Cardinals on Wednesday, Peter Schrager of NFL Network reports.
Jones tallied two stops in the Bears' 17-9 loss to the Packers on Sunday.
Jones tallied four tackles, including a sack, in the Bears' 16-13 win over the Panthers on Thursday.
Jones tallied three tackles in the Bears' 29-13 loss to the Vikings in Week 18, and ended the season with 52 tackles, three sacks and a fumble recovery over 17 games played.
Jones tallied a sack and six tackles in the Bears' 41-10 loss to the Lions on Sunday.
Jones tallied a sack and a tackle in the Bears' 29-22 loss to the Vikings on Sunday.
Jones doesn't have an injury designation for Sunday's Week 5 matchup against the Vikings.
Jones (hip) was a limited participant during the Bears' practice Thursday.