They owe around £800,000 to the Inland Revenue, with controversial owner Alex Hamilton - a man who admits he only bought the club because of the redevelopment potential of its Racecourse Ground - refusing a series of takeover bids.
Fans fear he wants the club to go into administration, so that he can sell their stadium for anything up to £12million.
But the club have been given until December 3 to find new investment, and must return to the High Court on that date to avoid being closed down.
It means that United's may have to wait until that afternoon before finding out whether they will be able to play their FA Cup second round clash with them - the match is scheduled to kick-off at 7.45pm.
Director Dave Griffiths said: "We've had a couple of tentative enquiries after the appeal on Tuesday, as you would expect, but nothing concrete.
"We've now got two weeks to find a buyer, and after Saturday's home game against Bristol City we'll sit down again with the accountants and see where we go from there."
He admits that club owner Hamilton is the man who will decide the club's fate.
Griffiths added: "He holds all the cards, although it's difficult to know what's happening with him at the moment because he's not answering his phone.
"I think he's just holding on for liquidation so he can seel the ground on, but as things currently stand we live to fight another day."
Iron fans attending Saturday's game at Bristol Rovers are being asked to wear red, or hold up a red card, in a show of solidarity with Wrexham supporters as part of a national day of action.