David Cameron approached Football Association chairman Greg Dyke about running for London mayor before Boris Johnson successfully contested the position in 2008.
The former BBC director general said he was told by the Prime Minister's former strategy director Steve Hilton that it did not matter that he was a former Labour supporter, according to the latest claims in a biography by Lord Ashcroft and journalist Isabel Oakeshott.
The talks eventually broke down after Mr Dyke asked to run on a joint ticket with the Liberal Democrats, according to the book.
According to the latest extracts in the Daily Mail, Mr Dyke said of the mayoralty: "I was first contacted by Steve Hilton, who I liked a lot because he was not like a traditional Tory.
"I had just left the BBC and they obviously thought this would be clever.
"I said to them, 'I am not a Tory'. "To which they basically said, 'It doesn't matter'.
After a meeting with Mr Cameron, Mr Dyke concluded he could not run on a Tory ticket and the idea of running with the Lib Dems idea was floated and approved by the PM, but eventually dropped.
Mr Dyke said: "I said I thought the jump was too far. I said I quite fancied the job, but I can't do it."
The Call Me Dave biography is proving embarrassing for Mr Cameron, with lurid claims about a bizarre Oxford initiation ceremony involving a dead pig and condemnation from military chiefs for his response to crises in Syria and Libya.
Meanwhile, according to the BBC, Mr Cameron reportedly responded to Lord Ashcroft's claims at a fund-raising dinner by suggesting he was being "stabbed in the back" for failing to offer the former Tory donor a senior ministerial position following the 2010 election.