The Gers boss met with the new chief executive this week to discuss his playing budget as the club attempt to balance the books and move forward after months of off-field uncertainty.
And he is confident the board won't make rash decisions when slashing costs. He said: "Graham said at the AGM that there would need to be cuts, so that's fine. He's made that public. He hasn't made it known to me where those cuts are going to take place, and in what shape or form.
"Graham is aware that, in an ideal world, we would be building a team and a squad for next season, and hopefully the years after. It would make sense to Graham and he has said it that, contrary to what people have said, just cutting and selling is not the right way to go about it - in terms of the progression of the club, the team and the squad going forward.
"He's aware of what could have an adverse effect as much as a positive effect - short-term and longer-term."
Despite raising around £22million in their stock market flotation just over a year ago, Rangers are once again facing money difficulties after they posted a loss of over £14m for the last financial period.
Wallace could look to shave a seven-figure sum off McCoist's budget and the Gers boss knows savings have to made.
He said: "If you need to take one step back to take two or three forward again, that will be Graham's decision.
"We can't go down the same road we were on before. The stability of the club moving forward is of paramount importance.
"The fact there was nothing concrete coming out the first meeting would indicate the importance of the situation.
"Graham is certainly fully aware how important the decisions made just now will be for the short, medium and long term."
Fears have risen among fans that the board could look to cash in on key players this month in a bid to stem Gers' losses.
Lee Wallace and Nicky Law are two of the Light Blues' most valuable assets, but McCoist, whose pay cut has now been ratified by the board, is determined to retain them.
He said: "I don't want to lose them. But these decisions aren't getting made myself. First of all, someone would need to make an offer for them. And then that offer would need to go to the board. I would be thrilled if there were no bids for anyone."