Mr Rivera, a Fox News Channel roaming correspondent-at-large, suggested on Twitter that he may consider throwing his hat in the ring to campaign for the position of the retiring senator.
“Pondering running for retiring @senrobportman seat in United States Senate. #GoBuckeyes,” he wrote on Twitter on Wednesday.
Mr Rivera, 77, has lived in Shaker Heights, Ohio, since 2017, according to Bloomberg, and has hosted a radio show Geraldo in Cleveland since 2018.
The broadcast journalist was a staunch supporter of former president Donald Trump until their relationship fractured following the 2020 election.
Mr Rivera criticised the former president for his actions in the wake of his loss of the presidential election, claiming that since the election he had “behaved like an entitled frat boy.”
The correspondent had stood as a longtime friend and ally of Mr Trump and supported him publicly over his four-year presidency.
Sen Portman, a Republican who entered the Senate a decade ago, announced in late January that he will not seek re-election in 2022, citing deepening political divisions.
“We live in an increasingly polarized country where members of both parties are being pushed further to the right and further to the left, and that means too few people who are actively looking to find common ground,” the two-term senator said in a statement.
“This is not a new phenomenon, of course, but a problem that has gotten worse over the past few decades,” he added. “This is a tough time to be in public service.”
Additional reporting by Reuters
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