Lawyers for Jeremy Skibicki had asked that his jury trial, which is set to begin Wednesday, be heard instead by a judge alone.
The defence argued that two years of publicity surrounding the high-profile case may have biased the jurors.
A U.S.-based psychologist who has studied jury bias told court this week that news coverage of the slayings of the four women has been consistent and emotional.
Skibicki's lawyers said they plan to argue he is not criminally responsible for the deaths because of a mental illness.
Skibicki has pleaded not guilty to four counts of first-degree murder in the deaths of Rebecca Contois, Morgan Harris, Marcedes Myran and a fourth unidentified woman Indigenous leaders have named Buffalo Woman.
The partial remains of Contois were found in a garbage bin and at a city-run landfill in 2022. Police have said they believe the remains of Harris and Myran are at a different, privately owned landfill outside of the city.
The location of the unidentified woman is unknown.
