Talks are understood to be taking place over the controversial concept with Newcastle United owner Mike Ashley to rename the stadium the Sports Direct Arena as part of a big-money deal.
The idea has been floated by Green since his consortium took over the club, but it has been met with a mixed reaction from supporters. Many are against the idea at all costs while others see accepting the money for selling the rights as more important.
Ibrox was one of the first football stadiums to open back in 1899 and Johnstone is reluctant to see the name being changed.
He said: "It is one of those situations where your heart is telling you one thing and your head is saying something completely different.
"While I understand the financial reasons for looking into such a deal, I need to be honest and say I wouldn't like to see it change.
"It will always be known as Ibrox to me and perhaps I'm a bit old fashioned, but that is the way I would like it to remain.
"I know other clubs have changed the names of their stadiums such as Manchester City, but I'm not completely in favour of it happening right now.
"Maybe a few years down the line it will be different. But right now Rangers are attracting huge crowds in the Third Division, there is a share issue which will also bring in a lot of money so is there that great a need to do it right now?
"If Rangers are back in the SPL then surely they will secure a far greater deal for selling the rights as they would now?
"I know Charles Green is looking into every way possible to raise money to try and take the club forward and he is making a lot of progress.
"But he might face a bit of resistance with this one. Let's get the club out of the Third Division and back into the top flight before we look at this.
"If such a deal is going to bring in something like £10million and help sign a few top quality players once the club is back in the SPL then the fans might accept that is the only way possible to build a new team and give it their backing.
"But my advice just now would be to sit tight and look at it again further down the line."