The lawyer for Truro City's administrators says there is a preferred bidder for the financially-stricken club that could put down a £50,000 bond to secure its future.
James Moore told BBC Radio Cornwall there were two bidders hoping to take over the Blue Square Bet South club.
The Football Conference wants the bond in place by 1700 BST on Thursday or Truro face expulsion from the league.
"We have two interested parties but have one preferred bidder," Moore said.
"They're at a position where the bond could be satisfied by the deadline.
"No buyer is going to put down £50,000 if they aren't comfortable that they're going to be able to acquire the the club and trade it going forward," continued Moore, from lawyers Walker Morris.
Should Truro fold and their results be expunged, the bond would cover the travel costs of clubs who had already played them.
But any deal is subject to the bidders being able to reach an agreement with the club's creditors and secure a long-term lease at Truro's Treyew Road ground.
Moore said they would be "working flat out" during Wednesday and Thursday to try and ensure the purchaser was comfortable enough to formalise the bond.
"It's definitely more promising than last Thursday, but I don't want to put anyone under any illusions, these are two big obstacles.
"There has been a lot of progress made, but there's a lot that needs to be done," he continued.
"The position we're in now is much better than we were in last week, but it's still a long way before we're able to put the bond down and have a sale to go through."
Truro have been since August after owner and left the club to fight
They were initially told they had to pay their bond to the Football Conference by but were given
But even if the bond is paid by the bidder, it may be some time before the sale actually goes through.
"If that bond were put down, it doesn't mean a sale's completed," Moore added.
"It means the purchaser is satisfied that the main outstanding issues for a sale to complete have been largely dealt with to give them comfort to put £50,000 at risk and have the confidence to complete a sale in the near future."