A reporter at The Undercurrent secretly recording video which captured Mr Jordan claiming that he spoke with Mr Trump "yesterday" and that the former president would soon announce his 2024 candidacy.
"Yeah, I talked to him yesterday. He's about ready to announce after all fo this craziness in Afghanistan," Mr Jordan said.
The congressman also said Joe Biden was "really bad" and should "resign."
On Thursday, Mr Jordan joined a number of other high-profile Republicans during a visit to Iowa. During the event, he said he was "convinced" Mr Trump would run again.
Mr Jordan's office denied the comments to Politico, despite the fact that the congressman was apparently caught on camera making the statement.
"Not true. Mr Jordan did not say this," a spokesperson said.
Jim Jordan: President Trump, he's gonna run again.
Pete: You think so?
Jordan: I know so. Yeah, I talked to him yesterday. He's about ready to announce after all of this craziness in Afghanistan... pic.twitter.com/Ndogdm7Ipl
— Lauren Windsor (@lawindsor) September 3, 2021
Mr Jordan is the second Republican caught on video making comments they have had to walk back in the past week.
Senator Ron Johnson was secretly filmed blaming Mr Trump for his own election defeat in 2020.
"So we obviously counted enough Republican votes. The only reason Trump lost Wisconsin is that 51,000 Republican voters didn't vote for him. They voted for other Republican candidates," he said.
He also admitted there was "nothing obviously skewed about" the result of Wisconsin's election, despite backing an audit of the state's ballots.
Mr Trump is still Republicans' favoured presidential candidate.
A Reuters/Ipsos poll released on 21 May found that only 28 per cent of Republicans opposed Mr Trump running again in 2024.
Most Republican respondents to the poll – 63 per cent – say they believe Mr Trump's fraudulent claims that the election was stolen from him in 2020.
Despite the loyalty of his Republican base, Mr Trump's approval ratings among the public is dismal. According to an NBC News survey of adults in April, Mr Trump's approval rating was only 32 per cent, and his disapproval rating was 55 per cent.
While Mr Trump is far and away the favoured candidate to win a Republican primary, without a significant change in approval he could once again fail to secure the presidency in 2024.
Mr Trump lost teh popular vote by more than sevn million in 2020, and by 81,000 votes in the electoral college. Nonetheless, more Republicans voted for Mr Trump than for any other Republican in history.
Polls suggest Republicans' second most-favoured choice for president is Florida's Governor Ron DeSantis, whose state has seen a massive increase in coronavirus cases thanks to the spread of the Delta variant.
Mr DeSantis has not yet announced any intention to run for the nation's highest office.