Wallace is standing for re-election at next week's annual general meeting and McCoist believes his pledge to give fans more involvement in the running of the League One side is the ideal way to take the club forward.
Wallace, along with current board members Brian Stockbridge, James Easdale, Norman Crighton and David Somers, is battling to see off a challenge from a consortium led by former oldco director Paul Murray at the AGM at Ibrox on December 19.
Speaking on Thursday, Wallace said: "What I am concerned about is having the stability and the opportunity to take the club forward and we need to have that mandate.
"We will have a wide range of supporters engaged with us in the run-up to the AGM and they want to know the club is in good hands with people in the boardroom who genuinely have Rangers at heart.
"I can categorically give them that assurance from the CEO's chair. My focus, 100%, is to drive this business forward."
And McCoist threw his weight behind Wallace's vision for the future, saying: "I think the very least our fans deserve is a voice.
"I think without doubt they have kept the club going with their incredible support so the more they have a voice and an opinion that can only be a good thing.
"Like anything else there will be a lot of agreements and disagreements but I do like what Graham is saying in terms of listening to the fans."