Former Sheffield United chief executive Charles Green has signed an "irrevocable" agreement with Rangers' administrators Duff and Phelps and majority shareholder Whyte after weeks of negotiations. But King's claims cast doubt over the anticipated sale of the ailing Glasgow giants to Green's consortium.
"It was verbally agreed over lunch but is legally valid," King told BBC Scotland.
"It suited him at the time and I will hold him to it."
He added: "I have first option on (his) shares and would not forgo this unless I was absolutely certain that any proposed transaction, that excluded me, was in the best interests of the club. I have yet to see such a proposal."
Whyte, who has an 85% stake, has dismissed King's comments.
South Africa-based businessman King, the second largest shareholder in Rangers, added: "I stayed on because I also had my investment and those of the other minority shareholders to protect and I believe that my presence on the board prevented Whyte from getting away with more than he even did."
In response to King's comments, Whyte told BBC Scotland: "If the CVA (Creditors Voluntary Arrangement) is successful the minority shareholders will retain their shares in a club that will be a debt-free sustainable business and not the basket case that I inherited as a result of the mismanagement of the previous board."