Stillitano says Rangers and Celtic need to recognise their global appeal or else risk hampering further growth.
Stillitano has backed staging Old Firm games outside Scotland
Relevant Sports chairman Charlie Stillitano, the man behind the upcoming pre-season International Champions Cup, believes the Old Firm derby has to be taken outside of Scotland in order to maintain its global appeal, the Daily Record has reported.
Stillitano believes the ageing generation of Celtic and Rangers supporting expats across the world means interest in the fixture outside of Scotland is in danger of slipping over the next few years.
Last season's promotion for Rangers sealed their return to the Scottish Premiership after financial problems forced them to reform at the bottom of the league pyramid four years ago, although a dramatic Scottish Cup semi-final last term acted as a timely reminder of the rivalry's magnitude.
Kenny Miller scores the first goal for Rangers in last season's Scottish Cup
And Stillitano believes the fixture, which dates back to 1888, has outgrown Scotland, adding it is well primed to thrive in front of an international audience.
He said: “You don’t want it to wither on the vine here. There’s only five million people in Scotland. You’re not going to have 50 million any time soon. There’s millions of Celtic and Rangers fans across the world and there has to be some recognition of that.
“We want to host it away from Scotland, whether that is Wembley, Asia or North America."
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The Old Firm derby is one of the fiercest contests in world sport but Stillitano, who attracted controversy over comments made about Leicester City's rise to the Champions League, insists security would not be a concern, even if it was hosted at Wembley.
“We did Manchester United-Liverpool in Miami. Great game and there was no trouble.
“There was a lot of fun ribbing and that was it. We are also doing the Manchester derby in Beijing.
Rangers manager Mark Warburton celebrates winning the Scottish Championship with the trophy
“Why not export Celtic-Rangers? It makes perfect sense for me. I’d like to do it every year, or at least every couple of years.
“It’s completely safe in North America but I also think that it could be managed at a place like Wembley.”
Stillitano also has ambitions to make the ICC tournament into an annual event between the winners of the English Premier League and the Scottish Premiership, hinting it could be akin to England's Community Shield.
"Anything you can do to make it special. Maybe it can be done on its own, perhaps like the Charity Shield in England," he added.