The ultimatum follows hard on the heels of a law suit by Facia's main backer, Israel's United Mizrahi Bank, against former staff over alleged backhanders received for arranging loans of over pounds 8m to the retailer.
"We have written to the directors and their solicitors. We think now is the time to get on with this," KPMG partner Tony Thompson said at the weekend.
"We will give them more time. If nothing happens, say within 10 days we will have to consider a compulsory petition for winding-up."
UMB's move, revealed yesterday by the Independent on Sunday, is the latest in a raft of legal action surrounding Mr Hinchliffe and Facia's collapse with pounds 70m of debts in June. Sources say he will also shortly be interviewed by the Serious Fraud Office, which raided his Sheffield home in August.
In writs issued last week, the bank is seeking damages and the return of alleged illicit payments via Malibu Management Corporation, a British Virgin Islands company, to three ex-employees at its London branch.
UMB, represented by City lawyers Nabarro Nathanson and barristers David Richards QC and Matthew Collins, is expected to return to the High Court today to extend injunctions granted last week.
The money is alleged to have been paid by South London property trader Robert Leckie, who is understood to have introduced Mr Hinchliffe to UMB and received at least pounds 1.3m of commissions on loans advanced.
At the weekend, Mr Leckie's solicitor insisted the introductory fees were legitimate and refuted the allegations that backhanders were subsequently paid via a Malibu account at Credit Suisse in Switzerland between October 1995 and January this year.
But he admitted Mr Leckie had had financial dealings with the employees, who include Rafael Kellner, the former head of UMB's London branch.
Mr Hinchliffe declined to return calls to discuss his relationship with Mr Leckie and UMB.