Reports suggest Newcastle owner Mike Ashley is in talks with Light Blues chief executive Charles Green over a lucrative deal that would promote his Sports Direct retail firm.
Rangers are also reportedly considering other stadium re-branding proposals.
A similar move proved to be unpopular with Newcastle fans and McCoist expects the Ibrox faithful to be split on the issue.
He said: "I can appreciate it's a really delicate issue and I would imagine it would split fan opinion.
"I've got to be honest and say I'm pretty open-minded about it.
"At the same time, I definitely think the fans would certainly have to have a voice and an opinion on the final decision.
"We saw the reaction of the Newcastle fans when it happened down there and I'd imagine a good percentage of our support would feel the same way.
"My own opinion is that I'm neither for or against it - I'm reasonably open-minded.
"I do understand the business side of it but I do understand, more than anything, history and tradition."
Ashley's brand is already an official retail partner of Rangers but McCoist was unable to confirm the businessman's interest in Ibrox naming rights.
He added: "I don't really know the strength of interest, that's a question you'd have to direct at Charles.
"I don't know the ins or outs or the proposal as such.
"No doubt, when I sit down with Charles over the next couple of days, he'll keep me up to speed on it.
"It's a decision that thankfully won't be mine. I'll have an opinion on it, the same as every other fan, but the decision won't be taken by me."
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