The group known as No Labels has indicated that it would like to run a third-party challenge to both President Joe Biden and former President Donald Trump.

Yet in a move that is likely to leave Trump happy, one prominent GOP figure recently said that he is dropping his name from consideration. 

Sen. Bill Cassidy "never seriously considered" running for president

According to The Hill, Louisiana Republican Sen. Bill Cassidy said during an appearance on NBC News's "Meet the Press" this past Sunday that he has no interest in running on a No Labels ticket.

"I was never seriously considered to be their candidate. It was reported in the press otherwise, but I was never seriously considered … The answer is not," Cassidy told host Kristen Welker.

WATCH: @SenBillCassidy (R-La.) says he was “never seriously considered” by No Labels as a potential presidential candidate for the group.

But Cassidy credits the speculation to his belief that "neither candidate is actually offering serious solutions" right now. pic.twitter.com/BAJLMXdspj

— Meet the Press (@MeetThePress) March 18, 2024

"On the other hand, the very fact that No Labels did, that was floated, I will say has a certain rationale to it," Cassidy stressed.

Cassidy criticizes Trump over recent comments

The Louisiana senator went on to praise No Labels' organizers  for wanting "answers to serious problems in our country," adding, "And right now, neither candidate is actually offering serious solutions."

"So the very fact that I speak about that means that, wait a second, this might be somebody whom we would consider. Because this person is talking about serious, serious answers to serious problems," he stated.

Cassidy has long been known as a critic of former President Trump, at one point telling Welker that Trump's decision to question the humanity of violent foreign criminals "reflected poorly" on him.

He also slammed Trump's pledge to pardon some of those who were convicted of crime relating to the January 6 riot on Capitol Hill, say that it will "be a wrong signal."

Former Georgia Republican lieutenant governor won't run either

Cassidy's announcement came just days after former Georgia Republican Lt. Gov. Geoff Duncan revealed that he too will not be running for president under the No Labels banner.

"After careful deliberation, I have withdrawn my name from consideration for the No Labels presidential ticket," The Hill quoted Duncan as saying to The Associated Press.

Meanwhile, The Hill reported last week that No Labels is planning to unveil its presidential candidate later in the month.