George Letham, Douglas Park and shareholder George Taylor want to buy all 40,739,000 shares due to be issued in a fundraising offer in January.
But current shareholders must be allowed first refusal on maintaining the size of their stake.
The trio have provided club chairman David Somers with proof of funding.
Letham has previously loaned the Championship club money while Park, the owner of coach hire firm Parks of Hamilton, is one of Scotland's most successful businessmen. Taylor already owns 3.2% of the club.
The three businessmen emailed their offer - which included two representatives being appointed to the board - to Somers immediately after the club's annual general meeting at Ibrox on Monday, but before the results of the shareholder vote were known.
The proposal was also sent to the company that oversees Rangers' listing on the Alternative Investment Market and Rangers' lawyer, while the Scottish Football Association has also been informed.
In their annual accounts, the Rangers board revealed the business needs at least £8m of fresh investment in January to continue trading for the next 12 months.
Ashley is keen to raise his stake from 8.92% to 29.9% but that request, made on the behalf of the Newcastle United owner by new Rangers chief executive Derek Llambias, was rejected as it contravenes SFA ownership regulations.
An offer from Dave King, a former Rangers director, also remains on the table.
Ibrox Stadium Attendances at Ibrox have been dwindling this season
At the AGM, a resolution allowing the directors to hold a share issue was passed.
However another, which would have allowed new investors to buy all of the available shares without them being first offered to existing shareholders, was rejected.
A non-shareholder can still underwrite the share issue or current shareholders can apply to purchase more shares than they are entitled to buy to maintain the size of their stake.
"We find it disturbing that resolution failed to gain approval," said a spokesman for the consortium.
"Everyone knows the company is in dire need of investment and yet shareholders represented on the board decided to vote against investment from new shareholders.
"Presumably they believed the SFA would clear the way for Mike Ashley to increase his holding, but we now know that this was not approved.
"The SFA would have been aware there is a credible alternative and we would like to make sure the fans are aware of that, too."
The three men believe that, as existing shareholders, they can still secure a significant holding and insist the funding is in place.
"We are trying our best to do what is right for Rangers and the supporters," added the spokesman. "Why on earth would anyone not want a hugely successful businessman like Douglas Park involved?"