Originally, the Union Rescue Mission had hoped to get a contract with the city to operate it, but the mission says it could not meet additional requirements the city wants.
The move comes one week after the ACLU of Arkansas criticized the pending deal over the mission's policy of only hiring evangelical Christians to run the center.
Little Rock's Mayor says that's no longer an issue.
"We have other faith-based organizations that the city contracts with, some people raised some questions about that, that is off the table because the money issue is not working out," Mayor Stodola said.
The mission's executive director says this was solely a business decision and had nothing to do with its hiring policy being criticized.