An alleged conversation between a "senior Liberal cabinet minister" and former NSW premier Gladys Berejiklian was relayed live on air by Channel Ten's political editor Peter Van Onselen yesterday.
Berejiklian reportedly described the Prime Minister as a "horrible, horrible person", with the minister responding he was a "complete psycho".
The ABC has not seen or verified the text exchange.
Berejiklian has not denied the conversation, but said yesterday she had no recollection of it.
Asked again about the messages today, Morrison said he had not spoken to Berejiklian, but they had a good relationship.
"It's always been very positive and I think we've worked very well together," Morrison said.
"Of course people say nasty things about you as Prime Minister all the time.
"Just switch on your social media feed and you'll get yourself quite a giggle, I get one all the time, it comes with the job."
Morrison repeated that he could not respond to the substance of "anonymous" messages.
He said he had "confidence" the reported Liberal minister was not in his cabinet.