English clubs voted against that proposal in 2009 but Irish businessman Desmond, who once held a stake in Manchester United, thinks it is an "inevitable" outcome eventually.
"We would like to compete in the Holy Grail in England," he told Sky Sports on Wednesday.
"It will bring money into Scotland and rekindle football in Scotland having (Manchester) United, Arsenal and others.
"Maybe it's going to be 10 years but I think it's inevitable.
"Rangers and Celtic are among the top 10 teams in Britain and some of the biggest teams in the world and they should be competing at the highest level.
"I think it's inevitable there will be changes."
At the time of the 2009 vote, the Premier League chief executive Richard Scudamore said, "It's a non-starter.
So we've made a clear and unequivocal statement and we're going to move on from there. No means no."
Since then, Scottish football has suffered from Rangers being demoted to the bottom division in 2012 after a financial crisis, losing their regular fixtures against Celtic with a consequent decrease in gate money and television receipts.
Currently leading the Championship (second tier), they hope to renew the so-called Old Firm rivalry next season.
In the meantime Celtic have won the Premiership easily for four years in a row, giving the pair exactly 100 Scottish League titles between them. No other club have been champions since Aberdeen in 1985.
Celtic manager Ronny Deila added his support to Desmond's at a news conference ahead of Thursday's Europa League game against Fenerbahce.
"It's not easy to do things very quickly in Britain, it takes time," he told reporters.
"But Celtic is a team that should have the opportunity to play in the best league and hopefully in the end we can get into the (English) Premiership or a league that is more of a British thing."
While the big two might like to test themselves in England, however, there has been resistance from English clubs concerned that introducing two new teams at the top level would mean others having to drop lower down.
(Reporting by Steve Tongue, editing by Alan Baldwin)
Share
