PHOENIX (AP) The other two are former Cincinnati city manager Milton Dohoney Jr. and Oakland city administrator Deanna Santana.
Final interviews for the job will be on Feb. 19.
Zuercher is a 20-year city employee and has been acting manager since David Cavazos left the job last October.
Naimark has worked for Phoenix for 26 years.
He previously was an executive assistant to the city manager and the City Council.