London Evening Standard/London

The mayor admitted he regularly thought about carrying on at City Hall and had even consulted friends on the possibility.

However, City Hall insiders insisted afterwards that he would “definitely” not be standing again in 2016.

Johnson, hosting his first Ask Boris show on LBC radio, has previously always ruled out running for a third term and possibly becoming London’s longest-serving mayor. But he told listeners: “The truth is that there are so many things I’m trying to do at the moment that I know we’re not going to get done in time by 2016.

“I won’t deny it — it is something I think about. It’s something that I’ve even talked to friends about.”

Johnson admitted he would leave the capital’s top job “very reluctantly” in three years’ time but when pressed about his plans by presenter Nick Ferrari he rowed back.

“The reality is that after eight years you’ve been at it for a long time. You see what happens to people who do things for too long,” he said, adding: “The truth is I’m stepping down in 2015 and who knows what will happen.”

He added there would have to be a “pretty massive” public call of hundreds of thousands of Londoners for him to stay on — “a sort of reverse (Egyptian President) Morsi”.

His public admission that he has even considered the possibility will give hope to some supporters who would like his administration to continue.

Sources close to the mayor have told the Standard they think there is still a possibility he could change his mind, depending on how his other future plans pan out.

Johnson is widely believed to want to return to Parliament to take over the Tory leadership from David Cameron, although as he has pledged to stay on as mayor until the end of his term the timing could be against him.

In words that are unlikely to go down well with Tory colleagues, Johnson repeated his call for an amnesty for illegal immigrants who have been in the country for more than 12 years. “We effectively have it anyway. Why not be honest about what’s going on?” he said.

Johnson also urged Londoners to “grow up” about fracking as he offered up London’s streets to firms wanting to solve Britain’s energy crisis.

Johnson said on LBC Radio: “If we have those resources in the South-East let’s be grown up about it. It may be that some people will benefit mightily from doing this.”