The South Africa-based businessman will sound out shareholders about a possible rights offering.
And the Glaswegian will then fly to Scotland for a meeting with the club board.
He will also talk to Gers fans about how to withhold season ticket money from Rangers next season.
King said: "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 how they would feel about a rights issue.
"Also, whether they would participate and whether they would give the rights to someone like me. 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."
King claimed he was ignored when he warned the Rangers board about an impending financial crisis at the end of last year.
He said: "I told them: 'It's now early enough to anticipate you will not make the end of the year on your current cash balances. Let's try to go about a new fund-raising exercise'.
"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 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."
Meanwhile King has reiterated his belief that an anonymous figure is running the club.
He said: "There are powers behind the throne who would prefer someone like myself not be part of the future funding of the club."