King invested heavily in Rangers during Sir David Murray's reign and is reported to have lost £20million when the club went into administration in 2012.
But the Glasgow-born tycoon is now free to invest in the newco Rangers after settling a long-running tax dispute with South African authorities.
King said in a statement released by Rangers: "I confirm that I held talks with Rangers chief executive Craig Mather and finance director Brian Stockbridge in South Africa.
"The discussions were, to my mind, very positive and it was agreed that subject to the normal regulatory approval I would put my name forward to join the board and to serve as chairman.
"Such an appointment is of course subject to the approval of the existing board members and ultimately the shareholders of the company.
"There are also mandatory regulatory requirements that must be complied with and take time. I have already submitted all the necessary documentation."
It had been speculated that King wants former director Paul Murray to rejoin the Rangers board, but he stressed: "My involvement is not linked in any way to any other individual, albeit I have my private thoughts as to certain individuals that might add value to the club going forward.
"Ultimately it is for the shareholders to make such decisions."