McCoist and Wallace arranged the meeting to discuss the football department, including the manager's budget for close season transfer activity and the creation of a new role, chief football operations officer, to boost the manager's support staff.
McCoist has been mocked for repeatedly supporting figures who were subsequently discredited - Craig Whyte, Charles Green and Craig Mather - but he also endorsed Wallace despite the supporters group The Union of Fans and former director Dave King calling for him to be suspended pending the outcome of a police investigation for allegedly misleading the club's shareholders. When asked if Wallace had been straight with him, McCoist said: "Absolutely. Everything he's said to me, it's been completely up front. Everything he's said."
It was in the business review Wallace released on Friday that the creation of a new role, chief football operations officer, was revealed. McCoist welcomed the development in principle but he had firm views on how any sort of director of football, even by another name, should be allowed to operate.
"I know that sometimes these guys effectively sign players. I'm not sure that's a good idea. But if the manager tells him which talent to identify then I think that's a good idea. That's the best way to operate.
"There's no point in someone identifying talent that the club or team don't want, or don't need; that would go without saying. But if he was identifying talent which the football staff want then that would be a good idea."
Rangers used to have two full-time scouts plus four working part-time across England and Northern Ireland. Now there are none. "Things are all over the place," said McCoist. "We don't have a scouting department at the moment. It is in absolute tatters. We need help with scouting, with the medical department and with everything.
"I don't know what [a director of football] would cover. It might cover some of that. I'm just hopeful now that the report is out we can address some of these things that have been needing addressing for a long time."
Meanwhile, McCoist defended the vast majority of Celtic and Rangers fans after the negative publicity of crowd disorder at Monday night's Glasgow Cup final at Celtic Park. McCoist was in the main stand for the under-17 game - Celtic won 1-0 - but said he had been unaware of the problems which happened behind him, towards the back of the stand.
Smoke bombs and a flare were discharged during the game and seats were broken. PoliceScotland said three arrests had been made.
"I didn't see it, although I heard about five bangs," said McCoist. "I saw some flares. It's disappointing, particularly at a young boys' game. I believe that, before we went into administration, [behaviour at] the Rangers and Celtic games was getting better. I'm not the police and I don't know the figures, but there was a better feeling.
"The vast majority of Old Firm fans know what's right and what's wrong. There's a very small element who make the news and they are the ones we see and read about."