Rotherham, believed to be £1.5m in the red, have gone in liquidation because of "unsustainable indebtedness".
A club statement said the directors felt uncertainty over funding for the coming season meant they had no choice but to "throw in the towel".
If a buyer does not come in by 1700 BST on Friday, the club will close.
"We've had a great time with (chairman) Mike Yarlett's support but we know he hasn't got bottomless pockets," said Rotherham coach Mike Schmid.
He added: "We just hope a new owner can come forward to keep the spirit alive and would like to appeal to any interested party to make themselves known so that rugby can continue to be played in Rotherham."
The Titans were due to begin their new season in National League One on 4 September, but with the players believed to gone without pay for more than a month, the club's ability to fulfil their fixtures is in doubt.
Rotherham had to withdraw from last week's Middlesex Sevens and a friendly against Ulster because of a lack of cash.
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We cannot keep asking our shareholders to keep pouring funds in for little return
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Rotherham statement
Relegated from the Zurich Premiership last season, the club have been in financial turmoil ever since with creditors - including Customs and Excise - seeking immediate repayment.
A South African consortium pulled out of a deal after the Rugby Football Union (RFU) refused them permission to move the club to London for the 2005 season.
The club, who failed to win a single match in the Premiership last season, have been in dispute with England Rugby Limited (ERL) over the promotion of National League One champions Worcester.
The club's statement continued: "Players and backroom staff have been informed of the situation and are obviously distraught.
"Their livelihoods are at stake, and like the directors, they are hoping for a new investor to come forward.
"We have been trading for some time with a high level of debt which we felt was just about manageable, if we had either retained our position in the Premier division or had found a new investor.
"Unfortunately, some of our creditors have decided they can wait no longer for their cash, and have started proceedings to recover the money.
"Key among these is the Customs and Excise people, who are looking for the payment of a VAT bill.
"The club's directors have been battling for what seems like years to get top-level rugby established in Rotherham, but feel we've been knocked back repeatedly on promotion and relegation, on whether we could have an academy, and a whole host of other matters.
"We cannot keep asking our shareholders to keep pouring funds in for little return."