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David Moyes is keen to reignite interest in the League Cup and called for a revamped version to feature Scotland's top-flight teams.
Premier League teams have been criticised for not taking the competition serious and the League Cup has faced increasing pressure with the amount of football played in a season.
But Moyes believes that the competition could be rebranded the 'British Cup' with the arrival of the Old Firm and could be seen as more profitable for TV companies.
"Folk might shoot it down, but I think the opportunity to introduce the Scottish teams would give it a chance," the West Ham boss said.
"Maybe one of the TV companies -- if you're calling it the British Cup -- might be a bit more interested and it might bring in a bit more money.
"I don't think that down here the clubs like Celtic and Rangers are given enough credit for the size of their football clubs.
"I would argue there are only maybe two clubs in England bigger than either of them.
"We've just come out of one of the worst periods of Brexit. Why can we not actually bring Britain together and have a British Cup instead of a League Cup?
"I think what you might do is bring bigger crowds, certainly from Scotland."
Pep Guardiola, who has won the League Cup twice with Manchester City, recently suggested the competition should be axed to ease pressure during the festive period.
"Eliminate competitions, take out this competition," the City boss said.
"So less games, less competitions, less teams, more quality, less quantity. People can live without football for a while. It's too much.
"Start the season later after the summer. We have one game a week for a long time and then, after, we start having two or three in one week.
"In February it is one week [playing], one week [playing], two weeks off.
"We have two games in two weeks then, after, we have 72 games in one week. It's a little bit strange."
Liverpool boss Jurgen Klopp also slammed the League Cup schedule back in October, which eventually resulted in the Reds playing two matches 24 hours apart in December.
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