They owe the Inland Revenue £800,000, and they face going into liquidation if their petition for administration is not accepted.
Club owner Alex Hamilton has rejected two takeover offers from the supporters trust, but is considering an offer from a consortium which includes two former chairmen and two former managers.
Current Dragons boss Denis Smith knows the club could be unable to field a side in the cup tie at Glanford Park on December 2.
He said: "To be blunt about it, there's got to be a question mark over whether we'll be able to fulfil the tie. But we're hoping for good news on Wednesday which we hope will at least give us another two weeks' breathing space.
"It's a cloud hanging over us, and obviously it's not the best atmosphere in which to be a manager or a player but the lads have been brilliant.
"It's an extremely complicated situation and Hamilton is clearly not interested in football, or the people who work here. If we can somehow change that with a solution, then hopefully we can stave off the threat of liquidation.
"At the moment it's 50/50 whether we can achieve that, but i'm always positive and will look to the positive 50 per cent and not the negative."