King was snapped going into a city centre office while shareholder Sandy Easdale was pictured arriving at Ibrox stadium.
Last week, King said he would fly in from South Africa and wouldn't leave Scotland until he comes up with a "definite game plan" for the future of the Ibrox club.
The South Africa-based businessman urged supporters last week to withhold season-ticket money and hand it over to the club on a game-by-game basis amid growing concerns about the League One leaders' finances and governance.
The 58-year-old Glaswegian, who invested £20m in the club before it was consigned to liquidation in June 2012, made his plea to the fans after Rangers confirmed it had accepted £1.5million in loans from shareholders Sandy Easdale and Laxey Partners
King accepted an invitation to meet the Rangers board after an open letter from chairman David Somers claimed his "statements and innuendos" were "very damaging to the club" although he mocked the tone of the letter, saying he was being "summoned" to explain his comments.
Safe in the knowledge he has the backing by the influential Union of Fans coalition, it is thought King first flew into London to meet with investors in the club before travelling to Glasgow where, aside from his showdown with the Ibrox board, he will also meet supporters to find a way forward for the Govan club.
He previously told Sky Sports News, "I will now meet the board as requested. I will visit the institutions in London next week and put a schedule together with some of the existing shareholders to understand where they are and how they would feel about a rights issue.
"Also, whether they would participate, whether they would give the rights to someone like me and I would like that out of the way before I meet the fans.
"Then I will stay up in Scotland for as long as it takes until we have a definite game plan as to how we will go forward from there."
Rangers' former finance director, Brian Stockbridge, claimed last October that the Ibrox club would only have around £1million of its cash reserves left by April but chief executive Graham Wallace has been at pains in recent days and weeks to deny there is a risk of a second administration.
King claims the Ibrox board were fully aware of their financial predicament when they refused his offer of help towards the end of last year.
He said: "I said then 'it's now early enough to anticipate you will not make the end of the year on your current cash balances and let's now try, and in an orderly fashion, go about a new fund-raising exercise'.
"I was happy to be a significant investor, in fact a leader of a consortium putting new funds into the club with the only condition that the funds went into the club.
"I wasn't interested in taking on existing shareholders and buying their shares out.
"I was looking for a new share issue and for those funds to go into the club and into the team and really all that's happened is they have adopted a 'Nero fiddling while Rome burns' approach where the inevitability of the next couple of months has come to pass.
"The board has done nothing, has not been transparent at all with regard to the finance and we now know as a matter of fact 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 their rescue.
"They are looking for them to give enough money for season tickets so they can continue for another couple of months before again ending up in another financial crisis. That is what I am trying to avert at this point.
"The board has said my intentions are nothing other than damaging but in fact the opposite is true. The board should go to the fans and say 'this is the true state of the position at this club'."
King later clarified that he had offered to invest in Rangers in response to a brief statement by Easdale, which was read out on Sky Sports News.
The statement read: "Sandy Easdale refutes all claims that Dave King has made any offer of financial assistance to Rangers via him. These claims are wholly untrue."
In a statement, King said: "I refer to Sandy Easdale's statement earlier today that I had never had discussions with him regarding putting new funds into the club.
"I subsequently engaged in private communication with Sandy and he has confirmed directly to me that he intended his comment to be construed as meaning that I had never offered loan finance to the club. 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 that I do not believe that the club can afford debt at this time. Shareholders should be backing the club with equity and not debt.
"I accept that Sandy's incorrect statement was merely a misunderstanding and that he was not intending to impugn my integrity."
Meanwhile, Rangers boss Ally McCoist is praying Dave King can strike a peace deal with the Rangers board and end the Ibrox off-field saga once and for all.
He said: "I won't be privy to any of the meetings but I just hope that we can all move forward afterwards.
"Like any Rangers fan, I would be very hopeful the outcome would be positive and then we will see what happens after that."
McCoist again refused to discuss the specifics of the rumbling row but did admit it had been a distraction to his job of managing the team.
"Both the board and Dave have said it is best that I concentrate on the football," said the club's all-time record scorer.
"A few months ago, it was perhaps part of my job to get involved [with the off-field matters]. But now that there is a proper board in place and Graham Wallace there as chief executive, that side of things will be left to them.
"I'm not sure if that makes my job any easier but it certainly allows me to focus 100 per cent on the football, which in all honesty I haven't been able to do in the past. If that is a criticism of myself then so be it.
"You hope things would calm down and they have calmed down a little bit. But obviously there are still ongoing issues and I appreciate that.
"But I have to say I think the club is in a far better place than it was this time last year. Now we just need continued improvement on and off the park and that's what we hope to do.
"[If this was all put to bed by the time we were back in the Premiership] would be ideal but all we can do is concentrate on the football. The off-the-field stuff will look after itself. There are other people to deal with that."
The main aim of King's trip is to force the board to sanction a new share issue which will allow him to plough fresh cash into the club's dwindling coffers.
And the man who lost a £20million investment when the club was liquidated in 2012 will have his bid backed by the Union of Fans group, who plan to distribute 30,000 blue cards to the Ibrox faithful as part of a display urging the board to accept King's offer of help.
But McCoist again refused to take sides as he said: "I have no thoughts on that at all. That is not something I can control. I will let the fans, the board and Dave King and all those issues handle themselves. I won't get involved and nor will the fans want me to.
"Does the protest affect us? No, as long as it doesn't affect their support the team I won't mind, because that has been outrageous over the past two years."
Rangers clinched promotion to the Championship with a 3-0 win over Airdrie on Wednesday night.
The victory gave them an unassailable 26-point lead over Saturday's opponents Dunfermline but McCoist knows tougher challenges await his side next term.
"We have got the job done comfortably with eight games to go," he said. "We've achieved our target for this year but it will be very difficult next year.
"But nights like Wednesday mean everything to the people at the club and the supporters.
"To have well over 40,000 there on a Wednesday night at the same time as Barcelona are on the television is an unbelievable crowd.
"The title is payback for the fans. We want to give them what they want - a winning team."