In an interview with BBC1's The Andrew Marr Show, he said that he would like to see the public given the chance to vote on the issue before the next general election in 2015 although he did not expect it to happen.
"We have never had a popular vote since 1975 on a European question. I would like to be able to campaign for a single market and the withdrawal from a lot of the nonsensical policies," he said.
"I think it would be a good idea if they did it before 2015. It would be fantastic. I can't see them doing it before 2015."
Mr Johnson said that while he would prefer Britain to remain in the EU, it should be prepared to walk away if it was unable to negotiate a new relationship.
"I don't think that is necessarily the end of the world," he said.
"Don't forget that 15 years ago that the entire CBI, British industry, the City - everybody - was prophesying that there would be gigantic mutant rats swarming out of the gutters in the sewer to gnaw the last emaciated faces of the remaining British bankers if we didn't go into the euro."