The third division side, which has reportedly been losing £20,000 a week, applied for voluntary administration at a court hearing in Leeds today.
The club is being represented by insolvency firm Jackson Jolliffe Cork at the hearing and has been working with club chairman John Batchelor for the last two weeks.
Unless a buyer is found in time, York City could play its last game on 18 January against Swansea, and may go bust even quicker if the application fails.
To date, Leicester City, Port Vale and Barnsley have all applied for administration, while clubs like Watford have had to take drastic measures to avoid collapse.
Steve Absolom and Will Wright from KPMG Restructuring have been appointed joint administrators to City Motor Holdings and associated companies
Partners from Johnston Carmichael have been appointed as joint administrators to Axon Well Interventions Products UK
Begbies Traynor have been appointed administrators of William Anelay Ltd, York, one of Britain’s longest-established construction and heritage restoration companies
Smith & Williamson has been appointed administrators of charity 4Children