It is not known whether a vote will be taken on the issue but, if so, it is believed it would need the backing of 14 of the 20 clubs.
Mustering that level of support appears unlikely but Birmingham boss McLeish reckons the Old Firm will move south sooner or later.
Joining Everton's David Moyes, Aston Villa's Martin O'Neill and Tottenham's Harry Redknapp in supporting the proposal, he told the Scottish Sun: "I have always thought it would be fantastic to have Rangers and Celtic in the English Premier League.
"They are more than just clubs. They are enormous institutions who deserve to have a platform like that.
"Can I see a day when it actually happens? Yes, I can.
"And I've said for many years and even gone on record to say that TV money will have a big influence on such a massive move."
Former Rangers manager McLeish added: "I've always believed that the people who will be most influential when it comes to change are the TV companies, especially Sky.
"Yes, the football authorities like FIFA, UEFA, the FA and SFA have expressed opposition in the past. They argue letting Rangers and Celtic into England would open the floodgates around the world. They fear Dutch clubs would want entry into the Bundesliga or French clubs would want into Serie A.
"I understand those fears but Sky will have a major voice in the future of the game here."