• Sen. Lindsey Graham said Trump beats out Biden in terms of policy but not personality.
  • "If it's a personality contest, he'll be in trouble," Graham told CNBC.
  • Trump has teased a 2024 presidential run since losing the election in 2020, but he has not yet announced a bid.

Sen. Lindsey Graham said former President Donald Trump would be a strong contender in the 2024 presidential election if he could only curb his personality. 

Speaking in an interview with CNBC, Graham said he believes Trump "could be" the best person to represent the Republican Party in 2024.

"Whether you like Trump or not he was a consequential president," Graham said. "I think a strong American president — unpredictable — is a good thing as long as you keep it within the boundaries."

"His problem is personal, his policies have stood the test of time but has he worn the American people out in terms of his personality? Time will tell," Graham continued. "But I'll say this, after the Biden presidency, if there's a policy debate in 2024, I like his chances. If it's a personality contest, he'll be in trouble."

Trump has yet to announce a 2024 run.

But since losing the 2020 presidential election to President Joe Biden, Trump has said at various times that he expects to win in 2024 should he run in the next presidential election.

After losing, the former president began hosting a series of rallies that have served as a barometer of his popularity among conservatives and could help him maintain momentum for a potential campaign bid. During these rallies, he vowed that he'd be the president again. 

During an American Freedom Tour in March, for example, Trump promised to return to the White House in 2024.

"With the support of everyone in this room, we will take back the House, we will take back the Senate and we will take back our country, and then most importantly in 2024, we are going to take back our beautiful White House," he said, addressing a crowd of rallygoers in Fort Lauderdale, Florida.

In July, sources close to the former president said he's eager to announce a 2024 presidential bid. 

He "wants to clear the field and dare other people to run against him," one source said, per CNN.

Biden's aides said the president will think about 2024 re-election strategy after the midterm elections, as Insider's John Dorman reported.  

"The president has said he's planning on running again," White House senior advisor Anita Dunn told Bloomberg. "People should take him at his word."