King, who also accepted the Ibrox chairman David Somers' offer of a face-to-face meeting with the board, indicated that he wants to invest in exchange for new shares in the holding company Rangers International Football Club.
The South Africa-based businessman said he would be flying to the UK by the end of next week to discuss his plans with existing shareholders. Having arrived in Scotland, King insisted he would stay for "as long as it takes", not leaving until he had a "definite game plan" for the future of the Ibrox club.
The tycoon, who invested £20m in the club when it was under the control of Sir David Murray, said he had no interest in buying out the stakes of existing shareholders, as he wants to ensure new funds go directly to the club and the team.
However, the 58-year-old - who was once Rangers' second-biggest stakeholder - said he would make no new investment until there was full transparency over the club's financial affairs. He also echoed his call of last week for fans to place their season-ticket money in a separate fund amid growing concerns about the finances and governance at Ibrox.
While revealing his new investment strategy, he said the Ibrox board were fully aware of their financial predicament when they refused his offer of help last year.
King insisted he was "happy to be a significant investor, a leader of a consortium putting new funds into the club" but the only condition attached was the funds had to go into the club. "I wasn't interested in taking out existing shareholders and buying their shares out," he said. "I was either looking for a new share issue and for these funds to go into the club and into the team and really all that's happened is almost a 'Nero fiddles while Rome burns' approach.
"The board has done nothing, has not been transparent at all with regard to the finances. We now know that the club has run out of funds, and is trying to shuffle on in the hope that the fans will once again come to the rescue and give them enough money from season tickets so they can continue for another couple of months, before again ending up in a financial crisis. That's what I am trying to avert at this time.
"I am going in as a fan, but as a fan who is fortunate enough to be in a position to give very substantial funds in the club. I say to the club that I am there to support you but what is very important is, if we do invest money, we have to know where it's going and we still require transparency around the club's affairs."
Sandy Easdale, the Rangers director released a statement in response last night. "Sandy Easdale refutes all claims that Dave King has made any offer of financial assistance to Rangers via him," it read. "These claims are wholly untrue."
King then responded. "[Sandy] has confirmed directly to me that he intended his comment [to mean] that I had never offered loan finance to the club," he said. "He again confirmed that I had offered equity finance to the club when I met with him.
"Sandy is correct. I have only offered equity finance and I have stated repeatedly I do not believe that the club can afford debt at this time."