Investment banker Phil Maher has made a formal complaint to police, and allegations Wallace misled shareholders at the AGM in December could be looked into.
The former Manchester City official told shareholders at the AGM in December that the Glasgow club had enough money to see out the season.
Now South Africa-based businessman King has urged police to include other directors in their investigation.
The Scot has issued a strongly-worded response to the 120-day business review released to the Stock Exchange by Wallace last Friday.
The 58-year-old, who has stated he is prepared to invest up to £50 million of his personal fortune in his boyhood heroes, called the review "flimsy" and "completely superficial".
DAVE KING STATEMENT
I have taken time to carefully consider and reflect on this long-awaited business review. This flimsy review is completely superficial and could have been put together in a day by a relatively junior employee. It falls well short of the strategic business review that we were promised. There is nothing to read between the lines, no sign of a coherent plan to save this club, and more importantly no hope for the supporters or shareholders. I find it difficult that any CEO would expect this review to be taken seriously. I would reject it if one of my CEOs presented such a summary review to me.
I offer a number of personal observations on the review:
1 - It is seriously wrong for this board to state in the review that at the time of the AGM (December 2013) the board, and the CEO in particular, believed that there was sufficient cash to last until the end of the current season. The CEO is now subject to a criminal complaint on this very issue but I believe that his comments were made with the full knowledge of the board. Certainly no-one came out to contradict him. We should therefore expect any criminal investigation to extend to other board members. It is telling that Charles Green had to step down when under internal investigation and yet the CEO continues with his duties as before.
2 - If cash was wasted as a result of mismanagement (presumably Charles Green etc.) then what steps are being taken to hold management accountable for this?
3 - The board has conceded that it does not plan to effectively compete with Celtic in our first season back in the Premier League.
4 - This is a great review for Celtic fans. It is stated that the board might only raise £20million over the next three years. This paltry amount will guarantee that Celtic will be in a league of its own for the next few years - and possibly permanently thereafter. Celtic will continue to enjoy exclusive access to the Champions League windfalls and will go from financial strength to strength. The gap could become financially irreversible.
5 - The board still does not have a clear plan for raising capital despite knowing for some months that a financial crisis was looming.
6 - It is interesting that the credit card companies agree with me that the season tickets should not be released to the club. However, it is genuinely shocking that this board has, for several months, withheld the knowledge that fans would not have access to credit card facilities when renewing season ticket purchases. The board preferred to blame "external parties" in an attempt to hide this serious non-disclosure. How can this board ask fans to ever trust them again?
7 - The board continues the blame game and takes no responsibility for the current debacle. In truth, it is this board's stubborn refusal to secure fresh equity that is the cause of the present fragile state of the club's finances. The board clearly hoped to muddle along by using the season ticket advances from fans. This review should reinforce to fans that this board cannot serve as an appropriate custodian for their season ticket money.
8 - The board has admitted that Rangers is not presently a "going concern" and yet offers no plan on how this will be dealt with in the short term. Fans could once again lose their season ticket advances if given to the club at this time. It is unconscionable that this board has done nothing to bolster the finances since the last AGM.
In a statement released by Rangers on Monday night, chairman David Somers said: "Graham Wallace is working tirelessly and doing an excellent job in leading the rebuild of our football club by creating a Rangers our fans can be proud of.
"He will continue to develop the club's long-term future plan which will return us to the top of Scottish football and competing in Europe.
"Any suggestions of inappropriate behaviour by him in relation to his duties as Chief Executive Officer are odious and unfounded.
"They will be defended with full rigour, if a substantiated complaint is ever put to him or Rangers.
"The history and facts have been explained in both the Interim Statement and the Business Review summary.
"Any media reports to the contrary are based on rumour and gossip which is damaging to the football club.
"If Mr King wishes to engage in constructive dialogue, then the door remains open.
"Regrettably however, he continues to make fictitious, inaccurate and misleading comments which are very unhelpful."