A spokesman for Mr Turnbull said he had no memory of making the statement.

A source who knows Mr Turnbull well said he believed the two men could have made a successful political partnership in a similar way to Peter Costello and John Howard, whose tenure as treasurer and prime minister in the 1990s and 2000s was one of the most politically stable in modern Australian history even though the two men were not close personally.

Instead, Mr Abbott left Turnbull on the periphery of the cabinet as communications minister and kept Mr Hockey as treasurer even though his authority had been shot by the badly received first budget in 2014, his failure to deliver a surplus, and an off-hand comment that poor people drive less.

If Mr Abbott had switched treasurers after the failed leadership vote against him in February last year, he might have changed the course of political history. Mr Turnbull would have been unlikely to challenge Mr Abbott and his policy advocacy and popularity among wavering voters could have helped the Coalition catch up to the Labor Party in the polls.

The book, which will be published on Monday by Black Inc, describes Mr Abbott's inaction as he is repeatedly warned that supporters of Mr Turnbull's are preparing to remove him as Liberal leader.