Fleming, who may be in the running for another job, has reportedly been with Columbia since 1995.
In her job as director of the city finance department, Fleming's duties include financial planning, budgeting, treasury management, investments, purchasing, accounting, payroll, business licensing, insurance and utility customer services.
Fleming's resignation would mark the fourth high-profile departure from Columbia City Hall in a month. She follows city manager Bill Watkins; First Ward Councilman Paul Sturtz; and Fifth Ward Councilwoman Laura Nauser.
(Fleming photo appears in Columbia Tribune city leaders section.)