As reported in the Evening Times yesterday, Gers chief executive Charles Green has refused to rule out selling off the naming rights to the stadium, with SportsDirect tycoon Mike Ashley thought to be interested in a deal.
Any move to rename Ibrox would split the Light Blue legions and McCoist wants fans to have their say on the major decision.
He said: "It's a difficult situation in terms of finding the balance. Sitting in the seat I am at the moment I can see both arguments in terms of it being a very good business deal but, at the same time, it has always been Ibrox.
"It is a really touchy subject and it will hit a nerve with supporters up and down the country. I think there definitely should be dialogue.
"I think they have an opinion that should be heard and have a say in the final result.
"That decision will be taken by Charles and the businessmen in the club, but I think Charles would agree that fans have a voice and it should be heard.
"If it were to happen, my own opinion would be that I would like Ibrox to be in the name. I can understand other situations where Arsenal moved from Highbury and Man City from Maine Road to new premises.
"When you are keeping the same stadium, though, it is a different scenario."
Despite being hit with an SFA registration embargo in the summer, McCoist is on the lookout for players as the January transfer window approaches.
Rangers will be unable to field any new recruits until September 1, but the Ibrox boss is keen to shop around.
McCoist said: "We are looking at free transfers and players who are out of contract in the summer. It does give us an opportunity to get ahead of schedule in terms of signing players. That would be a big plus."
He added: "We need to strengthen the side and strengthen the squad. "