A judge already denied a request from Brendt Christensen's attorneys to delay proceedings until October, but said he would be open to a reasonable proposal. The trial was originally scheduled for September 2017.
Prosecutors are trying to prove Christensen kidnapped and killed 26-year-old Yingying Zhang in 2017.
Prosecutors are seeking the death penalty.
Christensen's attorneys said they needed more time to find a psychiatrist. The (Champaign) News-Gazette reports that defense attorneys say they've found a new psychiatrist who could be prepared by July 1.
Prosecutors have until Friday to respond. A Monday hearing is scheduled to discuss the trial date.
Information from: The News-Gazette, http://www.news-gazette.com