It emerged yesterday that the Ibrox club will hold a second share issue before August in a bid to raise £8 million.
And the union - an umbrella group which comprises six supporters organisations - has claimed Wallace is being "undermined from within".
A union statement read: "We are extremely concerned that there are now two distinctly different messages being sent out from Ibrox, which appear to be completely at odds with each other regarding our club's finances.
"They show the split in the boardroom and raise the question as to who is running Rangers.
"On the one hand, Graham Wallace has clearly stated that there is no financial crisis, while on the other hand there is a cash crisis which can only be resolved by an urgent share issue.
"The message sent out by Mr Wallace appears to be at odds with that of Sandy Easdale who has claimed that club finances were 'fragile'.
"Who are the Rangers fans to believe? Who wields the real power in the boardroom?
"If it is Mr Easdale then who is he taking his instructions from given his refusal to name the people behind Blue Pitch and Margarita, whom he represents?"
The Union of Fans have also asked why South Africa-based businessman Dave King, who has stated he is prepared to invest £50million in the Glasgow club, is being ignored.
The statement said: "If the board are indeed considering such a move, then will the shares be offered to all shareholders or just those represented by the current board?
"Also, why are they so reluctant, if finance is required, to speak to investors who actually care about the long-term future of the club?
"We have asked for Graham Wallace to come clean about the cash situation at Rangers and we repeat that request.
"Mr Wallace must make a statement to clarify his position and to explain the leaks of the last few days.
"The appearance is that Mr Wallace's authority is being undermined from within.
"The bottom line is very simply the question of who is running Rangers.
"Is it extremely well paid chief executive, Graham Wallace, or Sandy Easdale, a man who, for whatever reason, is not even a member of the plc board?"
Meanwhile, Rangers last night confirmed they have signed centre-half Darren McGregor on a year deal.
The former St Mirren defender, who is the second summer signing after Kenny Miller joined last week, was a free agent after leaving Paisley.