Paul Murray, who is seeking election to the Gers board at the AGM a week today, has reiterated his belief that Green is working behind the scenes. And former Light Blues director Murray has also refused to rule out the possibility that former owner Whyte has an agreement with Green.
He said: "We're reasonably confident that Craig Whyte doesn't have a legal claim over the assets between himself and Rangers.
"What we don't know is any side deals that Craig Whyte has with Charles Green.
"The 26% block of shares that the Easdale brothers have got is largely the original backers of Charles Green.
"So I am pretty sure that Charles Green is behind the scenes somewhere."
However, Wallace, the former Manchester City chief executive who was appointed to the same role at Rangers last month, has dismissed those accusations. And the 52-year-old Scot has the insisted the current directors of the Ibrox club all have the best interests of Rangers at heart.
He has also appealed to Gers supporters to give them the chance to help return the SPFL League One club to the forefront of Scottish football.
Wallace said: "Those individuals (Green and Whyte), who I have never met, I can categorically say have no involvement in the running of this club.
"The club needs stability. It needs the platform in order to be able to move forward. The AGM is a pivotal moment.
"There has been a lot of conversation over the recent weeks and months about the relative merits of particular campaigns and of particular areas of interest to individuals.
"What I am concerned about is having the stability, having the opportunity to be able to take the club forward and we need to have that mandate to be able to move the club forward."
Speaking to Sky Sports, Wallace added: "We will have a wide range of supporters engaged with us in the run-up to the AGM. They want to know that their club is in good hands.
"They want to know that we have got people in the boardroom that genuinely have got the interest of Rangers at heart and I can categorically give them that assurance.
"Sitting from the CEO's chair, my focus 100% is to drive this business forward."