This is despite the fact that prospective owner Charles Green has already stated that he has an irrevocable deal with Whyte for the transfer of his 85% shareholding in Rangers.
But according to reports King says he and Whyte agreed last year he would have first refusal on the shares "at whatever price anyone offers and Whyte is willing to accept".
But Whyte is reported to have insisted that King's assertion was categorically untrue.
"I have first option on Whyte's shares and would not forego this unless I was absolutely certain that any proposed transaction, that excluded me, was in the best interests of the club," he added.
King was one of the club directors identified in the Scottish Football Association's recent Note of Reasons for Rangers' transfer embargo.
He and his former fellow directors were criticised for not doing enough to highlight the non-payment of VAT and PAYE.