The club was bought by businessman Charles Green for £5.5million yesterday as it was plunged into liquidation.
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However, Mr McColl last night urged Mr Green to sell the club to his consortium, which also includes wealthy car dealership and coach hire business owner Douglas Park.
Mr McColl, a Rangers fan and one of Scotland's best-known businessmen, is lending his expertise to a bid which would see Ibrox hero Smith installed as club chairman.
He explained that he had "real concern" Mr Green's takeover would be a "re-run of what has happened before".
He added: "None of us have any confidence that it is a secure way forward for the club. We want to make sure it is in good hands, safe hands."
Mr McColl revealed his plans after another dramatic day in Rangers' 140-year history.
Mr Green's proposed company voluntary arrangement – which would have avoided liquidation – was formally rejected at a meeting at Ibrox lasting just nine minutes after HM Revenue & Customs announced it would not support it.
He then bought the club's entire assets through his "newco" firm of Sevco under a pre-arranged deal.
However, Mr McColl, who became one of Scotland's wealthiest men after building up the Clyde Blowers engineering empire, last night said: "I would like to issue a public appeal to Charles Green to strongly consider selling the club to the Walter Smith consortium.
"This would be in the best interests of Rangers, the Rangers fans, and all of Scottish football. Mr Green does not have the backing of the Rangers support and, the longer he delays, the harder the situation will become.
"I don't think he will get the fans' support or the players' support."
Referring to reports yesterday that manager Ally McCoist was to quit the club after falling out with Mr Green, Mr McColl said: "You saw the announcement about McCoist, indicating that Green was a wee bit duplicitous with him, if that's the right word. Alistair obviously had some issues."
Explaining his reasons for launching a bid to save the club, Mr McColl added: "I think there is real concern about the Charles Green bid and what might happen. A number of people have been approached by him. They feel uncomfortable about the way it is going.
"We wouldn't have come out with this if we had been comfortable, if the deal was going through, the club was being saved and everything was going to be hunky-dory. But I think there is real concern about this being a re-run of what has happened before.
"There is a real concern. The focus here is to make sure this is stabilised and safe, that is all. Rangers Football Club is far too important for Scotland, Scottish football, and Glasgow to be messed up again.
"Our bid is because the group that is involved want to make sure that it is in good hands, in safe hands.
"A number of the individuals in our group have great concerns because of their interactions with Green. The way it is going, there is not enough transparency. There is just worry, with all the club has been through. The group here has decided that something had to be done to fix this – to try to recover the situation with the club.
"The question we will be asked now is why didn't we come forward before.
"The answer is that none of us wanted to own a football club, but when we saw the way it is going, everyone has been forced to say, 'Look, we have to do something'."
Mr McColl refused to reveal how much money he was putting into the Walter Smith-led consortium, saying: "I don't want to comment about me or any of the consortium. I have no comment to make about who, or how much, or what. This is a genuine effort to support Walter Smith and the Rangers supporters to secure their club going forward."
Mr Green last night installed Malcolm Murray, a former pensions fund boss and an Ibrox season ticket holder, as chairman of Rangers and vowed the club "will rise again".
Mr Green also said he wants McCoist to remain as manager and "firmly believes he is the man to take Rangers forward."
But Rangers fans' chiefs last night urged supporters not to buy season tickets until Mr Green "steps aside" and allows Smith and Mr McColl's consortium to take control of the club.