The Apple CEO is described as a "control freak" in the story reported by Business Insider over the weekend.
BI quotes two unnamed "mobile industry execs," who claim Apple rejected a Adidas creative concept for the third time, leading to the decision to drop the campaign.
Apple has been criticised for keeping a tight control on the creative aspects of the platform, something advertisers aren't used to.
Apple introduced the iAd mobile advertising network on 1 July, claiming AT&T, Best Buy, Campbell Soup Company, Chanel, Citi, DirecTV, GE, JC Penney, Nissan, Sears, Target, Turner Broadcasting System, Unilever and The Walt Disney Studios amongst those who had signed up for the scheme.
According to Apple, the iAd network reaches millions of iPhone and iPod touch users around the world, and is a highly desirable audience for advertisers. Payment for the ads takes place directly through iTunes Connect, Apple's iTunes publishing portal, with developers keeping 60 per cent of all revenues.
BI adds: "An Apple rep did not comment, but has not denied that Adidas has pulled out of the iAd program. (And, to be sure, perhaps Adidas had really lame ideas, and Apple was right to reject them.) Adidas did not respond to our request for comment."