Mr Graham made the comments during an interview on Fox News Radio program "The Brian Kilmeade Show".
Mr Graham would not say that Mr Trump lost the election, but said if the president were to "fall short" that he should continue with a second run and not "let his movement die."
"I would encourage him to think about doing it," Mr Graham said. "Grover Cleveland came back. Donald Trump should think about it if he falls short."
Mr Graham said Mr Trump should consider creating "an organization, platforms over the next four years to keep his movement alive."'
Mr Graham won his fourth Congressional term on Tuesday after defeating Democrat Jaime Harrison.
The South Carolina senator isn't the only one who has floated the idea of Mr Trump running again in four years.
Rick Gaetz, a campaign aide from Mr Trump's 2016 campaign, told USA Today that Mr Trump would "seriously consider another run in 2024."
Mick Mulvaney, the former White House Chief of Staff, also said that he would include Mr Trump on any shortlist of Republicans expected to run for office in 2024.
Mr Trump has not commented publicly about running in 2024, though a recent Axios report suggests the president is considering the option. He has yet to concede the election to Mr Biden, and is still adamant that he can retain the White House.
The president plans to challenge the election results - which he baselessly alleges are rife with fraud - through a series of legal challenges. He has openly stated that the Supreme Court - and its majority of conservative Justices - should decide the results of the election.
Mr Graham said that he expects Mr Trump to continue fighting the results of the election.
"I talked to the president for a long time yesterday. He wants to fight, and he should fight. ... If we can close the margins in Arizona and Georgia and look at provisional ballots, this is not over," Mr Graham said.
Despite the senator's optimism, it's extremely unlikely that that scenario would occur; if anything Mr Biden is on track to end the election with 306 electoral votes.
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