Dominick's has put a number on the possible job losses when the grocery store moves out of the Chicago market late next month.

According to a state report, the company may lay off up to 5,600 people.

The grocery chain, which will close any unsold stores Dec. 28, could shed 5,633 jobs in Illinois, including 3,244 in Cook County alone, according to the monthly Worker Adjustment and Retraining Notification Act, also known as the WARN report.

Parent company Safeway Inc. said last week that Dominick's employed 6,600 employees in Illinois.

Four stores have been sold to the private-equity owners of Jewel-Osco.

A spokeswoman for Pleasanton, Calif.-based Safeway did not return messages today.

According to the WARN report, four other Cook County companies have announced a total of 341 cuts.

Statewide, six Illinois companies added 375 layoffs to previous announcements and five announced upcoming cuts of 555 total positions, not including Dominick's.

The WARN report did not mention the closure of Joliet telecommunications company CommScope, as reported by the Herald-News Wednesday.