Speaking in Tamworth today, Mr Joyce said "like 3000 people" knew who the minister was.
"I would suggest that if you know anything about this, don't wait to be outed, out yourself," he said. "And give an explanation."
"Maybe it was a bad day in the office, I don't know. That's a better way to do it."
When asked today if someone in "his own team" was trying to undermine him, Mr Morrison earlier replied "no".
Mr Morrison said was "not fussed" by the texts, and said the person who allegedly sent them had not come forward and confessed.
He spoke kindly of Ms Berejiklian.
"I welcome her very kind comments that she made yesterday and that very much reflects the strong working relationship we've had," he said.
"The scuttlebutt that runs around Canberra, who cares?
"What people say in text messages and on Twitter, frankly, doesn't matter."
Speaking earlier today, Opposition Leader Anthony Albanese noted the text messages were purportedly sent during the bushfire crisis in the summer of 2019/20.
"These are extraordinary text messages from the people who know Scott Morrison the best," he said.
"These are people who have observed him.
"If people who are Liberal Cabinet Ministers think that, Australians will make their own judgement."