Judge Charles Burns on Friday set a July 24 date to rule on the request from William Balfour's attorneys. Cook County prosecutors and defense attorneys are expected to argue the motion that day. If the judge lets Balfour's conviction stand, sentencing is expected to follow.
Hudson's mother, brother and 7-year-old nephew were killed in October 2008.
Balfour was married to Hudson's sister, and prosecutors contend he shot the family members in a jealous rage because she was dating another man. A jury convicted him last month of first-degree murder and other charges.
Copyright 2012 The Associated Press.