McLeish and O'Neill have managed in the top tiers in Scotland and England
Alex McLeish has joined Martin O'Neill in adding his support to the idea of Celtic and Rangers joining the Barclay's Premier League in England.
Bolton chairman Phil Gartside will suggest plans for a two-tier league of between 36 and 40 teams on Thursday.
Aston Villa boss O'Neill said the Old Firm would make the league stronger.
And Birmingham manager McLeish said: "If it can be progressed, it is a tremendous prospect, but I still think it is very early days."
It will be the first time that admitting the Old Firm will be officially on the agenda of a Premier League meeting in England.
But there is no vote planned, with Gartside requiring 14 of the 20 clubs to support his plan if it is to become a reality.
I think it would make the league even stronger than it is. Celtic are just an unbelievable club, and Rangers also
Aston Villa manager Martin O'Neill
Gartside might also propose an Irish franchise along with the Old Firm could be invited into the second tier of the Premier League.
"I would love to see Celtic and Rangers getting a platform that would merit the institutions that they are," former Rangers manager McLeish told BBC Scotland.
"I don't want to appear disrespectful to other Scottish teams, but the size of the clubs mean they deserve more investment and backing and they would certainly get that in the Premiership.
"It is gathering a lot of momentum, but I have not found there is a real big push to move this forward.
"It would be a sensational move and, to see Rangers trotting out against Premier League teams every week, would be nothing short of phenomenal."
Premier League chief executive Richard Scudamore last month said he could not envisage the 20 Premier League clubs voting for the Old Firm's inclusion.
Stoke City owner Peter Coates, for one, has gone public to say that England's top tier does not need the Old Firm.
But O'Neill, a former Celtic manager, and McLeish followed Tottenham Hotspur manager Harry Redknapp and Everton boss Davie Moyes in backing the inclusion of Celtic and Rangers.
The Villa boss told BBC Sport: "I would like to see both teams in the Premier League.
"I think it would make the league even stronger than it is. Celtic are just an unbelievable club, and Rangers also.
"I don't think for one minute that the likes of ourselves at Aston Villa would sit back and think 'that's it, we'll just give up'.
"I think all clubs would try to get stronger because of it."
Former Birmingham City chairman David Gold suggests that Gartside's proposal is the sort of radical idea required to save clubs from spending beyond their means to ensure Premier League survival.
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