Saudi chiefs have raised the prospect of entering the elite competition.
And Staveley can see it happening, when speaking at the Bloomberg Power Players' Summit.
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Staveley said: I'm quite sure there will be a Saudi club in the Champions League before long. Knowing Saudi, I don't think it will take too long."
Asked if there's interest in buying a stake in a Saudi club, Staveley added: I think that would be a lovely idea!
It would be a fantastic opportunity. I love the league and I've seen it develop. It's really exciting to see the competition really growing."