Brian Kennedy insists the Blue Knights' bid for Rangers stands and he has been informed he will hear by Friday morning whether it can proceed.
Kennedy says his lawyer held a meeting with administrator Duff & Phelps and was told it would "revert to us with an answer one way or the other" by Friday.
The offer is the same as the one beaten to preferred bidder status by Bill Miller last week.
"To clarify, we were asked to get to a quantum, which we did," said Kennedy.
"And, having been told it was acceptable, we made a written offer."
Joint administrator David Whitehouse on Wednesday claimed the Blue Knights' bid fell far short of the one withdrawn this week by American trucking tycoon Miller.
Whitehouse rejected former Rangers director Paul Murray's assertion that the consortium had been told their offer met the demands of the bidding process.
"For David Whitehouse to say otherwise is a slur on the character of Paul Murray," Sale Sharks owner Kennedy told BBC Scotland. "Paul doesn't tell lies.
"If someone else makes a bigger offer, that's fine. But it's about deliverability, not just quantum.
"The administrators chose the wrong horse when they went with Bill Miller.
"I wouldn't like to see them make the same mistake again."
On the subject of deliverability, Duff & Phelps has stated that a Company Voluntary Arrangement - the Blue Knights' preferred option of exiting administration - will be difficult to achieve in a short timeframe.
A number of financial analysts have also cast doubt as to whether a CVA, rather than creating a new company, is realistic at all.
However, Kennedy stressed: "Financially, a newco doesn't work unless you can write a cheque for £35m to compensate for the absence of European football.
"We would only contemplate a CVA."
Kennedy said it was his understanding that a CVA did not incur a similar three-year ban from European football as a newco.
He has been in discussions with Rangers owner Craig Whyte regarding the transfer of his shares.
Asked about the state of those negotiations, however, Kennedy would only say: "I won't comment on Craig Whyte's shares.
"I have a confidentiality agreement with Craig and I intend to respect that."