The former oldco director jetted into Scotland last week hoping to plough £16million into the crisis-hit club.
In return for that investment, King and his partners - former Blue Knight Paul Murray and wealthy supporter George Letham - wanted a 51 per cent stake in the club.
The Castlemilk-born millionaire held talks with members of the Light Blues board - but admitted his frustrations that he was unable to convince the “power behind the throne” to hand his consortium control.
The 59-year-old also had a telephone conversation with football board chairman Sandy Easdale, who controls around 26 per cent of the club’s shares, but said he was snubbed by Newcastle United owner Mike Ashley.
Ashley recently took his stake in the Ibrox outfit to just under nine per cent and has upped his bid for increased influence with the Glasgow giants by calling an emergency general meeting to remove chief executive Graham Wallace and Philip Nash from the club’s board.
But King questioned the motives of those pulling the strings in the Ibrox background.
He told Sky Sports News: “I believe I have made a compelling case for investment and for taking the club forward.
“I cannot see how a board, acting in good faith, can fail to recommend it to shareholders given the current plight of the club.
“Let the shareholders decide.”
King would have required the support of three quarters of the club’s shareholders in order to push through his rescue plan for a club that is due to run out of cash by the end of the year.
But with Easdale in command of 26 per cent and determined to hold onto power, the chances of a deal were always slim.
In a further statement, King - who lost £20 million when the League One champions were liquidated in 2012 - added: “Over the last few weeks Paul Murray, George Letham and myself have constructively engaged the Rangers board and (at the request of the board) Sandy Easdale regarding our proposal to invest £16million into the club as soon as is practically possible.
“When investing in any public company there are numerous regulatory and compliance requirements that have to be dealt with. There are also SFA compliance issues that arise when investing in a football club in Scotland.
“An obvious further complication in Rangers case is the seeming lack of authority of the Rangers board to make decisions without reference to key shareholders who appear to be ‘the power behind the throne’.
“Prior to commencing the implementation issues referred to above it is necessary to reach an in-principle agreement with the board that can then be put to shareholders. In this regard it is important to recognise that the so-called Easdale Block represents more than 25 per cent of the shares in issue and could therefore block the implementation of our proposal even if recommended by the board.
“Likewise, a combination of other shareholders could veto our proposal. I attempted to meet with Mr Ashley on my visit but neither he, nor his colleague, Mr Bishop, acknowledged my request for a meeting.
“This is their right but is unfortunate given the present concerns from supporters that Mr Ashley is using his shareholder status to put pressure on the board to alienate the rights and trade mark of the club in favour of his personal interest. I will make a separate announcement and appeal to fans on this topic at the appropriate time.
“Our initial proposal to the board was to invest the full £16million by way of equity at 20p per share. The board requested that we consider a debt/equity mix that would reduce dilution for existing shareholders and allow the debt component to be advanced prior to the extended time frame required for the approval of additional equity.
“We are amenable to this and to working with the board on the mechanics necessary to ensure that this is achieved provided that the full investment is recognised by way of board representation. We wish to appoint an equal number of members to the board and have the key say regarding the appointment of the Chairperson. We will not invest funds and let the existing board determine how these funds are spent. That has not worked well in the past.
“In any transaction of this nature there are a number of interests to be consulted and considered. The board has apparently engaged constructively on our proposal while advancing its own points as to what it believes is in the best interest of the club and its shareholders.
“Sandy Easdale has similarly apparently engaged constructively including highlighting some concerns. I have today responded to these concerns in writing. He will now consult with his co-shareholders and hopefully revert soonest so that we can proceed to agreement and the earliest possible implementation thereof.”