While the Easdales have manoeuvred themselves into the Rangers directors box, they still have an affiliation with their local Greenock side.
Sandy Easdale is a major shareholder in the Gers and is a member of the football board while his younger brother James is a non-executive director but both men have come under fierce criticism from Light Blues supporters in recent months.
Rae said: "I think they would like to control it and own it. It is not an easy thing to own.
"It is not like taking over Morton or St Mirren where you would have total control.
"The fact is, I don't think they will get total control at Ibrox and it won't satisfy them unless they do. They like to do things their way."
The Easdales have steadily increased their shareholding in Rangers since arriving on the scene at Ibrox last year.
And Sandy, who has a stake of around 4.5%, was one of the key players at December's AGM after being handed the proxy voting rights to the shares owned by Blue Pitch Holdings and Margarita Holdings.
RIFC plc shares are currently trading around the 31p mark and Rae reckons the Greenock-based brothers would like to plough more money into the Light Blues in the future.
"I never discuss with them whether they are going to be there a long while or a short time, but I get the impression that they want more and want to be the people who make the decisions. Whether the other directors allow that situation is another matter.
"There are a number of people who have got money, like [Dave] King, and he wants to rule the roost."
The Easdale's McGill's bus company is one of Morton's major sponsors and Rae, whose son Crawford is also a director of the club, admits he would be open to the prospect of them coming on board at Cappielow.
Rae said: "It had been my intention to talk with them. I am friendly with them and when they are down they always sit with us. I would be happy to have one of them, at least.
"But they are both in Rangers and it really depends the way the cookie crumbles up there.
"I am quite sure that I could get one, if not the two of them, if the Rangers thing fell through.
"But I don't see them moving from Rangers to Morton unless things don't go the way they want them.
"They have come up a hard way, they have got good business sense and know how many beans make five.
"I think they would be an asset for us. Crawford is friendly with them and has been to a few functions with them."
As well as their interest in Rangers, the brothers are still regular visitors to Cappielow and Ton chief Rae reckons their Ibrox tenure could be short-lived.
"I am not sure longevity will be the word to describe how long they will be at Rangers," Rae told SportTimes.
"They have got their own ideas who they would like in, the Rangers people, and I think they don't have the two of them in mind. That's only a gut feeling."