The South Africa-based Glasgow businessman was quoted in the Scottish Daily Mail on Friday morning, stating he had received no contact from chief executive Graham Wallace or the club's other directors in the past four weeks.
It was confirmed last Thursday that Wallace had asked McCoist's squad to consider a 15 per cent pay cut as he attempts to stem losses reported to be as much as £1million a month.
That plan was rejected by the players, but King, who lost £20million when the company which owned Rangers was liquidated in 2012, insists he is still ready to plough more money in to ensure the League One leaders are able to put up a fight upon their return to the Scottish Premiership.
Despite their current woes, however, the ruling Ibrox regime have yet to take up King's offer.
McCoist said: "The chief executive has said that he is certainly looking for future investment. I can't speak for Graham but if there was a potential investor, Dave King or whoever, it's safe to say Graham would sit down and talk to them."
Revelations of Wallace's pay-cut offer have sparked fears McCoist may be forced to sell off players in a desperate attempt to balance the books.
The club's all-time record scorer has held talks with Wallace this week but says there is "nothing concrete" to report on further cuts or player exits.
But King claims slashing McCoist's budget will only "render Rangers a small club in SPL terms for a longer period of time than need be".
The manager backed Wallace, who promised to undertake a 120-day review of the company at the club's annual general meeting last month, while insisting he will do his best to ensure the quality of his squad is not diluted.
"Graham has been completely honest, open and frank in the discussions that we have had," McCoist said. "I'm aware of the financial difficulties in the club but it's only fair to give Graham his 120 days that he has asked for and I'm confident that Graham will be the man to take us forward.
"From my manager's seat, I want to be very competitive when - not if - we get back to the top league. But as a fan, never mind a manager, I would want to be competitive in any league and particularly the top league when we get back there.
"I can understand every Rangers fan's concern. As manager of the club it's my job to make us as competitive as we can be and I aim to do that."
Rangers face Arbroath on Saturday in their final league match before the January transfer window closes. Unsurprisingly, McCoist is not expecting any new faces to arrive before then.
He said: "It's not been 100 per cent rubbished but I have been told it might be very difficult."
Striker Jon Daly insists the reason behind the Rangers squad's decision to reject the 15 per cent pay cut will not leave the dressing room.
Daly was asked during the Light Blues' weekly press conference to explain why that decision had been reached but declined to detail the squad's thinking.
"I don't think that is to be spoken about," he said.
"Whatever happens in the changing room, whether it's to do with finances or to do with tactical decisions, stays in the dressing room. As far as I'm concerned, that's the way it is going to stay."