Sunday's edition of El-Watan said its journalist had broken through security lines to speak to Mubarak on Saturday before his retrial on charges of complicity in the death of protesters killed in the uprising that swept him from office.
The paper, which is fiercely critical of Mursi and his backers in the Muslim Brotherhood, splashed the story on its front page, billing it as Mubarak's first comments to the media since he was toppled in 2011.
Lawyer Farid el-Deeb said he had sent Mubarak, 85, a message asking if the interview with the reporter had happened. "He sent me a message saying this didn't happen," he said.
"All of it is incorrect ... Mubarak did not meet with him or sit with him or any of this."
El-Watan said its journalist had spoken to Mubarak in a side room at the court where his retrial began on Saturday.
It quoted the deposed leader as saying it was too early to judge Mursi and expressing concern about the economy and lax security in Egypt, which he ruled for 30 years.
Deeb said the remarks appeared to be based on comments that he himself had made to the media.