The Herald-News reports that an attorney representing Kathleen Savio's family made the request on Thursday. The attorney said the judge should rule in the Savios' favor without a trial. Judge Michael Powers said he would make a decision within 30 days.
The 59-year-old Peterson, a former Bolingbrook police officer, was convicted in 2012 of killing Savio, his third wife, as they were finalizing a divorce in 2004. Peterson was sentenced in February to 38 years in prison.
Peterson's attorney Steve Greenberg and two other attorneys who had worked on his trial filed a motion last month to handle his appeal.
Peterson also remains a suspect in his fourth wife Stacy Peterson's disappearance in 2007.
The Associated Press contributed to this report.