The Rev. Jerome Warfield, head of the Board of Police Commissioners, said the board picked two search firms and expected the cost to be about $68,000, the Detroit News reported.
But Mayor Dave Bing refused this week to sign the two contracts.
"We were told the money is not there," Warfield said. "This was after we were guaranteed the money was there and that the contracts would be signed."
Ralph Godbee Jr. resigned as chief last month after his affair with a female subordinate became public. Chester Logan, the assistant chief under Godbee, has been serving as interim chief.
Community activist Ron Scott said the city needs a new chief soon.
"If we don't have a new chief soon, I'm afraid we'll lose momentum, and many of the things we're hoping for, whether it's improved services or a different culture within the Police Department, won't come to pass," Scott said.
Warfield said the board may be able to use money allocated for hiring a second assistant chief, in the search for Godbee's replacement.