Stephen Thompson revealed his concerns yesterday after pointing out the SPL club had gone from a £65,592 post-tax profit in 2010 to to a loss of £522,838 in the last financial year.
His fears centre on the fact that the Tannadice outfit has an absence of committed bank overdraft facilities after June 30.
They are backed up by auditor Deloitte, which said there was a "material uncertainty which may cast significant doubt" about the ability of Dundee United Football Company Ltd as a going concern.
United are £6.5 million in debt, with £5.4m from a loan, and the accounts reveal they were behind with their bank loan repayments by around £300,000. There was a 14% drop in revenues to £5.2m.
Mr Thompson said the ability of Dundee United Football Company Ltd to trade as a going concern was dependent on the "continuing availability" of appropriate banking facilties.
He added: "Having considered the company's forecasts through to December 31, 2012, the expected continuation of appropriate bank support and the continuing support of the controlling shareholder, the directors believe that the company will continue as a going concern through the next 12 months."