He also criticised Mr Morrison's bid to portray himself as the "daggy dad" from the suburbs during the election campaign.

"He's a professional politician who understands marketing and messaging better than most," Mr Turnbull writes in his memoir, A Bigger Picture, The Australian reports.

"His cringe-worthy 'daggy dad' persona is more exaggerated than it is conflated, but in net terms it probably helped.

"All that aside, however, the truth is that Labor lost the election that the coalition, after the August coup, did not deserve to win."

The former leader also blames Mr Morrison for leaks to media during a fraught examination of the tax system.

At one point, Finance Minister Mathias Cormann texted Mr Turnbull to say they had a "Treasurer problem".

The former PM preferred to work on policy in secrecy, seeing it as problematic to have ideas out in the public domain, good or bad, before they were fully formed.

"Scott, however, liked to start with a firm view of the solution - or, more often, the announcement - then go in search of the problem," Mr Turnbull writes, in a separate excerpt published in the Sydney Morning Herald.

"Plus, he confided in journalists much more than I thought was wise."

But he didn't believe it had been Mr Morrison's aim to damage or undermine the government.

Mr Morrison refused to engage on the characterisations of himself from his predecessor, or those recounted as coming from some among his cabinet.

"I am not interested in any distractions ... I'm interested in the health and well-being of Australians," he told reporters in Canberra during a press conference about the coronavirus.

Mr Turnbull described Home Affairs Minister Peter Dutton, a coup leader, as a "narcissist" and "self-delusional" for thinking he could be prime minister.

Mr Dutton is going to give the book a miss.

"I wish Mr Turnbull all the best in his retirement and I'm not going into a tit for tat," he told 2GB radio on Thursday.

Treasurer Josh Frydenberg says the memoir will likely end up on his bookshelf, but for now he is focused on the government's coronavirus response.

"I'm not going into the entrails of the past," he told Sky News.

"When I get a second I'll start reading books again."

Health Minister Greg Hunt says he won't be reading the memoir, which accuses him of regularly using abusive and vulgar language towards others.

"None of us are perfect, I absolutely acknowledge that," Mr Hunt said.

The memoir will be launched next Monday.

Australian Associated Press