As the former South Carolina governor Nikki Haley prepares to announce a run for president, a new poll found that just one additional candidate in the 2024 Republican primary will be enough to split the vote and keep Donald Trump ahead of Ron DeSantis, his only current close rival.

The Yahoo News/YouGov poll gave DeSantis, the Florida governor, a 45%-41% lead over Trump head-to-head. Similar scenarios in other polls have prompted increasing attacks on DeSantis by Trump – and deflections by DeSantis.

Speaking to reporters on Wednesday, DeSantis said: “I don’t spend my time trying to smear other Republicans.”

But the Wednesday poll also produced an alternative scenario involving Haley that may worry DeSantis.

Haley was ambassador to the United Nations under Trump before resigning in 2018. Having changed her mind about challenging her former boss, she is due to announce her campaign in her home state next week.

Yahoo News reported: “In a hypothetical three-way match-up, Haley effectively plays the spoiler, attracting 11% of Republicans and Republican-leaners while DeSantis’s support falls by roughly the same amount (to 35%), leaving Trump with more votes than either of them” at 38%.

When Trump first ran for the Republican nomination, in 2016, he did so in a primary field which was 17 strong come the first debate. Trump won the nomination without winning a majority of votes cast.

He ended his presidency twice-impeached and in wide-ranging legal jeopardy but he is still the only declared candidate for the nomination in 2024, having announced shortly after last year’s midterm elections.

Defeats for Trump-endorsed candidates cost Republicans dearly in November, particularly as the US Senate remained in Democratic hands, prompting some Republicans to turn against the idea of a third Trump nomination.

Haley is due to announce her run on 15 February in Charleston, South Carolina, before heading to New Hampshire, which also has an early slot on the primary calendar.

According to the Yahoo/YouGov poll, Haley attracted much more support than other potential candidates including the former vice-president Mike Pence, former secretary of state Mike Pompeo and Larry Hogan, a former governor of Maryland.

According to NBC News, Chris Sununu, the governor of New Hampshire and like Hogan a Republican moderate, is also preparing to run.

The Yahoo/YouGov poll said the same vote-splitting scenario played out with fields larger than three: the anti-Trump vote split and Trump therefore beat DeSantis. Other polls have returned similar results.

Art Cullen, editor of the Storm Lake Times in Iowa, the state that will vote first, recently told the Guardian: “These folks must be watching Trump’s poll numbers and that’s why there’s a delay [in announcements].”

“Trump and DeSantis are doing this sparring around the ring. Others are watching to see if somebody takes a blow and gives them an opening.”

But Sarah Longwell, publisher of The Bulwark, an anti-Trump conservative website, recently wrote: “Presumably the numerous candidates gearing up to run in the GOP primary understand that a fractured field benefits Donald Trump.”

“Are we sure they understand that they’d need to coalesce around a frontrunner by February 2024 to avoid the same scenario that gave us Trump in 2016?”