Discussions are ongoing over a deal to transfer shares from majority owners UBIG to a fans group, but the fact that the process has yet to be concluded has caused Bryan Jackson of administrator BDO to raise concerns.
It has been reported that BDO only have enough money to keep the club running until the end of the month, and Jackson concedes that they are almost at rock-bottom.
He has, though, vowed to continue to fight for Hearts' future.
"This is probably the lowest ebb we've got to," Jackson told BBC Scotland. "This deal should have been over the line by now.
"We have to accept now that there is a threat of liquidation and we are doing everything we can to avoid it.
"It (liquidation) is in absolutely nobody's interest - whether it's a creditor or a shareholder or a supporter - it can't be in anybody's interest, it just doesn't make any sense, and this is what we are struggling with.
"We just have to make sure it doesn't come to that."
Hearts staved off the threat of relegation from the Scottish Premier League with victory in the Edinburgh derby against Hibernian last weekend, but they still remain 19 points adrift at the bottom with seven games remaining.
