The date Saturday 9 October 2021 might go down in political history. Or at least that is what Donald Trump would like you to believe.

That night, Trump will hold a rally in Iowa, the celebrated launchpad for US presidential candidates, the state that goes first in the major parties’ selection process and that is already drawing potential contenders for the Republican nomination in 2024.

Trump’s ability to draw raucous crowds there will only fuel speculation that, despite his first term ending in defeat and disgrace, the 75-year-old intends to exact revenge by recapturing the White House from Democrat Joe Biden.

No one knows if this is true – quite possibly not even Trump himself. But the tease over 2024 suits Trump just fine on multiple levels. It keeps him relevant as the dominant figure in the Republican party. It keeps cash flowing from donors still devoted to his cause. And it flatters an ego that has always craved celebrity and being at the centre of attention.

“Look, this is a guy through all his life who’s been on the front pages,” said Henry Olsen, a senior fellow at the Ethics and Public Policy Center thinktank. “One thing he has learned is that nothing he experienced with the front page of the New York Post or The Apprentice or his books equalled anything like the constant attention you get by being an international political figure.”

It is hardly a surprise that Trump, perhaps the most unorthodox president in American history, should embrace one of the most unorthodox post-presidencies, eschewing the philanthropic works or presidential libraries that occupied those before him.

From his Mar-a-Lago estate in Florida, Trump takes a break from golf to issue emailed statements (he is banned from social media), give interviews to rightwing media and travel to campaign-style rallies in battleground states, all venomously attacking his successor and falsely claiming he was the true winner of the 2020 election.

At the rallies, when Republican politicians or supporters urge him to run again to right this perceived injustice, he keeps the prospect boiling tantalisingly by neither agreeing nor ruling it out. He also flexes his political muscles by endorsing pro-Trump candidates in various congressional races.

Such interventions would carry less clout if he formally pulled out of the race. So too would his blitz of emails that solicit donations to his affiliated political action committees. Trump raised more than $100m in the first half of this year, an unheard of figure for an ex-president. He comfortably outraised every other Republican on WinRed, the party’s major portal for online donations.

Olsen, author of The Working Class Republican, said: “If he were to say I’m not interested in 2024, whatever influence he wants to exert would be a dead letter. His real power comes from his ability to plausibly say, ‘I could be the president again’, so I think it definitely helps him maintain whatever influence he has.”

He added: “I’m sure it helps him with fundraising. Certainly if you’re one of the 5 million or 10 million people who just love everything he says and may have given him money in the past, the fact that he may be the next president certainly encourages you to give more small-dollar donations.”

Trump is watching the 2024 chatter closely and, although his wife Melania reportedly has little appetite for a return to the White House, is more than happy to stoke the flames. Earlier this month his camp emailed out the results of a Republican presidential primary poll for 2024 by Emerson that showed Trump on 67%, the Florida governor, Ron DeSantis, on 10% and former South Carolina governor Nikki Haley on 7%.

Anecdotal evidence from Trump’s rallies suggest that DeSantis, who has aped Trump’s hostility to the media, poses the biggest electoral threat. While most supporters remain fiercely loyal to the former president, occasionally one will say they would like to see him pass the torch to DeSantis.

Critics believe that this trend might be spurring Trump’s recent flurry of activity. Tara Setmayer, a former Republican communications director on Capitol Hill, said: “The rise of Ron DeSantis is a direct threat to Trump’s relevance. It’s no accident that you see Ron DeSantis constantly on Fox News.”

Setmayer, a senior adviser to the Lincoln Project, an anti-Trump group, added: “Trump sees Ron DeSantis as a direct threat to his popularity, and in his home state of Florida. Trump is a master communicator and marketer and he understands when a brand becomes stale so he needs to continue to say and do things that make him relevant.”

The uncertainty makes life awkward for other Republicans contemplating a run. Trump’s allies, who continue to push the lie of a stolen election, are working to create an air of inevitability around his nomination.

Congressman Jim Jordan of Ohio was recently recorded in an undercover video saying: “President Trump, he’s going to run again. I know so. I talked to him yesterday. He’s about ready to announce after all of this craziness in Afghanistan.” Jason Miller, a senior adviser to Trump’s 2020 campaign, told Cheddar that the likelihood that Trump will run again is “somewhere between 99 and 100%”.

There are still plenty of obstacles in the way of Trump’s audacious political comeback, however. He would be 78 at the time of the next election (though Biden would be even older). He was impeached twice and could yet face investigations over his role in stirring an insurrection at the US Capitol in Washington on 6 January.

Trump’s loss of power now deprives him, his family and his company of legal protections he enjoyed while in the White House. This summer New York prosecutors brought criminal charges against his property company, the Trump Organization and its chief financial officer, Allen Weisselberg, over an alleged tax scheme dating back to 2005.

But this too could provide a reason for Trump to keep alive the prospect of another run for president, based on the hope that the justice department would be reluctant to be seen as carrying out a politically motivated prosecution in an atmosphere of bitter partisanship. Any such move would be sure to provoke howls of Republican outrage.

At root, however, some observers suspect that the will-he won’t-he dilemma is simply about Trump’s insatiable desire to be talked about.

Kurt Bardella, a Democratic congressional campaign committee adviser, who believes Trump will run, said: “First and foremost, Donald Trump has an unhealthy need to be at the centre of attention. He is driven by pure ego and narcissism and running for the presidency satisfies a lot of those needs that he has. Win, lose or draw, just to be at the centre of attention and to be topical.

“We have seen throughout his entire life that, when you boil it down, everything he does is about that. Nothing burns him more than when he sees people like Ron DeSantis being labeled ‘the next Donald Trump’. I think he believes that the final chapter hasn’t been written yet and he’s not ready to turn the page or let anybody else, for that matter, turn the page.”