He has started trying to raise 100 million ($216 million) to create a kite mark that could be used by any food company to show they had reached certain standards for nutrition and ethical sourcing.
His ambition is that only firms that earn the kite mark will be allowed to sponsor or supply the Olympics, targeting the Tokyo 2020 tournament.
"More than anything - and forgive me if I am being romantic - but in our lifetime at the Olympics, which is the biggest theatre of all time, I want to see something with goodness at its heart on its billboards."
He said his team had spoken to the International Olympic Committee (IOC), which was receptive to the idea. "I want to get in the game as a premier-league sponsor. I don't want to fight with any of the other advertisers."
His attempt to reform the IOC's reliance on money from junk food firms - McDonald's has been part of the Games since 1976 and Coke has been a backer since 1928 - is his latest campaign to improve children's nutrition.
His TV series about school lunches was broadcast 11 years ago, and his controversial call for a sugar tax on fizzy drink was announced this week.
An outright ban on McDonald's or Coca-Cola at the Olympics, he said, was not his goal. But he hoped the companies would see the kite mark as an opportunity to improve their own standards.
He highlighted McDonald's British arm, which reformed its sourcing policy a decade ago.
"You have to ... say 'well done' to big businesses when they do good. And McDonald's probably props up the British organic milk industry, 100 per cent free range eggs, British and Irish ground beef."
