The Ten Network is reporting Ms Berejiklian and the unnamed minister messaged each other about Mr Morrison.

The former premier said the prime minister was a horrible person and he was more concerned with politics than people.

According to the text exchange, Ms Berejiklian said she did not trust the prime minister and that the prime minister was "actively spreading lies".

The cabinet minister also described Mr Morrison as a fraud and "a complete psycho".

"The mob have worked him out, and think he's a fraud," the minister said in a text.

The Ten Network also claimed some texts between the pair occurred during the Black Summer bushfires of 2019/20.

Ms Berejiklian said in one message that "lives are at stake today and (Scott Morrison) is just obsessed with petty, political point scoring".

In another message sent by the premier shortly after Mr Morrison's holiday to Hawaii during the bushfire crisis, Ms Berejiklian said she was "so disappointed and gutted".

When quizzed about the leaked messages following a speech at the National Press Club, the prime minister said: "Well, I don't know who you're referring to, or the basis of what (has been) put to me."

"But I obviously don't agree with it, and I don't think that is my record."

In a statement, Ms Berejiklian said she had no recollection of the text exchange taking place.

"Let me reiterate my very strong support for Prime Minister Morrison and all he is doing for our nation during these very challenging times," she said.

"I also strongly believe he is the best person to lead our nation for years to come."

It comes after the prime minister backed calls late last year for Ms Berejiklian to run for the Liberals in the federal seat of Warringah on Sydney's northern beaches for the upcoming election.

Ms Berejiklian resigned as NSW premier after being named in an investigation by the state's corruption watchdog.

She said she would seek a new role in the private sector and would not consider a move into federal politics.

Australian Associated Press