Attorney Keith Stoney, who is representing Cowley, said they asked for the continuance in order to have time to review documents that the city provided this week following a Tuesday hearing before the West Valley City Civil Service Commission.
Stoney said they have already reached out to the city to set a new date.
West Valley City spokesman Sam Johnson said the city was ready to go forward with the hearing Monday, and does not plan to settle with Cowley.
Cowley fired the shot that killed 21-year-old Danielle Willard during an alleged November 2012 drug bust. That shooting is reportedly not listed as reason for his termination. The Salt Lake County District Attorney's Office deemed the shooting of Willard was not legally justified. No criminal charges have been filed against Cowley in connection with the shooting.
The shooting episode sparked an internal probe of the narcotics unit after drug evidence dating back a year was allegedly found in the trunk of Cowley's patrol car, rather than the department's evidence room.
The probe revealed multiple violations, including that members of the unit had mishandled evidence, inappropriately used GPS tracking devices, kept trophies, or removed change and other property from suspect's vehicles.
Six of the officers have been disciplined; a seventh officer remains on paid leave in connection with the Willard shooting.
Cowley and former Lt. John Coyle who headed the narcotics unit are both appealing their discipline to the civil service commission.
During a hearing last month, Coyle claimed his discipline was overly harsh compared to other officers in the unit.
Coyle's demotion to the rank of officer resulted in an annual pay cut of about $20,000, said his attorney, Erik Strindberg, while people beneath Coyle were given "slaps on the wrist."
The three-member commission has not yet decided whether to reinstate Coyle to his former rank of lieutenant.