Dunphy told the Herald that he has "no interest" in taking over from Pat Kenny.
The controversial football pundit, who once fronted a chat show on TV3, said he would be "too busy" to host the Friday night programme.
"I've no interest, sorry. I'm not interested in it at all," he said today.
The former Ireland and Millwall soccer player was asked would he even be tempted if it was offered to him.
"No, I have no interest in the Late Late Show," he replied emphatically.
And O'Briain has revealed he doesn't want the job either.
The comedian said he wouldn't be a suitable candidate as he doesn't live in Ireland and no longer keeps abreast of the news here.
"That's why I wouldn't make a good Late Late Show host -- I didn't even know there was a bl**dy Budget happening," the London-based star insisted.
While Dunphy is a regular guest on the popular entertainment slot, it seems his experience on TV3 did not whet his appetite for the job. He took on Pat Kenny for the Friday night throne in 2003 but failed in his mission to topple the Late Late.
However, The Dunphy Show scored some notable successes, including having former Ireland captain Roy Keane as a guest.
Wicklow native O'Briain has hosted several RTE shows including The Panel but has lived in London for seven years.
Ryan Tubridy and Miriam O'Callaghan have emerged as the frontrunners to take over from Pat Kenny when he leaves the show at the end of the current season.
At the time The Dunphy Show was axed in December 2003, Dunphy said: "It's a difficult experience, to fail, but it's not the end of the world. It has to be seen in the perspective of people with tragedies in their lives. It's a light entertainment show, we took on a challenge, we failed, but we had a wonderful time trying to do it."
He said the "buck" stopped with him as he had made the decision to go head to head with the Late Late Show.
"You have to be fair to TV3. They're a commercial television station and the numbers have to stack up and probably in a healthier advertising market we would have been fine and would have been allowed develop the show."