The Football Conference yesterday announced that Truro City must satisfy "certain criteria" by 5pm on Thursday, October 11, to be guaranteed continued membership of the competition.
City are in administration and have suffered a ten-point penalty as a result, which sees them sitting at the bottom of Blue Square Bet South with minus two points after eight games this season.
Conference spokesman Colin Peake said: "Representatives of the Football Conference met on September 26 with representatives of Walsh Taylor Business and Corporate Recovery, the administrator of Truro City Football Club, and its legal advisor.
"The administrator and her advisor have been advised by the Football Conference that, to be guaranteed the club's continued membership of the competition, the Football Conference board requires the administrator to satisfy certain criteria by 5pm on Thursday, October 11, 2012.
"The matter is now in the hands of the club's administrator to meet these requirements."
It is understood that a number of parties have shown an interest in buying the club, although no offers have yet been forthcoming.
City's players, who have not been paid for several weeks, have stated that they will leave the club after next Tuesday's home game against Bath City if there is no change in the situation by then. They head for sixth-placed Chelmsford City today with manager Lee Hodges saying: "It's obviously not a good time for any of us.
"We are in desperate need of some positive news because what's happening off the field has major consequences for the staff, players and supporters. It's getting to the stage now where the players are finding it hard to keep their heads up, and I can understand that.
"I'm doing my utmost to stay as positive about all this as possible. I have to, for the players' sake, but you can see how it is affecting them, and that is bound to rebound on me."
Hodges' small squad is expected to travel without work-tied Danny Carne and central defender Calrone Hall (unavailable) and the City boss added: "It looks like it is going to be down to bare bones and 13 of us again.
"We're not in the best form or shape going somewhere like Chelmsford.
"In an ideal world you would want to be at your best going there, with a full squad and everyone competing for places at training."
Truro City (from): Sandercombe; Green, Williams, Hodges, Ash, Yetton, Afful, Broad, Cooke, Watkins, Moore, Martin, Hopkinson.