The New York congresswoman Elise Stefanik is “a killer”, Donald Trump reportedly said, amid a flurry of speculation around who might be his presidential running mate for 2024, after his crushing victory in the Iowa caucuses.

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Citing eight unnamed sources, NBC News said Trump discussed his options for a potential vice-president in Florida late last month.

Stefanik, a Harvard-educated 39-year-old former moderate who has risen in House leadership while aggressively supporting Trump, had just grilled leaders of Ivy League universities over alleged antisemitism on campus, a hearing that preceded the resignations of two of those college presidents.

“She’s a killer,” Trump reportedly said.

Steve Bannon, the far-right activist and alleged fraudster who was Trump’s campaign chair and White House strategist and remains a close ally, told NBC Stefanik was “at the top” of the running-mate race.

A “Republican campaign operative” said: “If you’re Trump, you want someone who’s loyal above all else. Particularly because he sees Mike Pence as having made a fatal sin.”

Pence was Trump’s vice-president, unswervingly loyal until he refused to block certification of election results in key states. On 6 January 2021, the former Indiana governor was forced to run from a mob Trump sent to the Capitol, some chanting that Pence should be hanged.

Witnesses to the House January 6 committee said Trump told an aide Pence “deserved” that fate.

Stefanik is now campaigning with Trump in New Hampshire, ahead of its primary on Tuesday.

Trump faces 91 criminal charges (for election subversion, retention of classified information and hush-money payments), attempts to keep him off the ballot for inciting an insurrection, and civil lawsuits over his businesses and a rape allegation a judge called “substantially true”.

Regardless, he won crushingly in Iowa and is favored to win in New Hampshire, despite a tougher challenge from Nikki Haley, a former governor of South Carolina.

Stefanik told NBC: “I’m not going to get into any of my conversations with President Trump. I’m honoured to call him a friend. I’m proud to be the first member of Congress to have endorsed his re-election, and he had a huge win in Iowa. So we’re very excited about that.”

The Trump campaign did not comment.

Haley is also the subject of running mate speculation, though Trump-adjacent sources told Politico they were against the idea.

“Nikki Haley as [vice-president] would be an establishment neocon fantasy and a Maga nightmare,” the far-right Florida congressman Matt Gaetz said, using an acronym for Trump’s slogan, Make America Great Again.

“On day one she would convert [the vice-president’s residence] into an anti-Trump resistance headquarters, undermining him at every step.”

Related: Nikki Haley plotted with Kushner and Ivanka to be Trump vice-president, Pompeo book says

Haley was US ambassador to the UN under Trump – and the subject of claims, including from the then secretary of state, Mike Pompeo, that she schemed to replace Pence as vice-president.

Trump’s oldest son, Donald Trump Jr, also told Politico he was opposed to Haley, because she “wants to be in every war the world has to offer”.

Lindsey Graham, the South Carolina senator who went from warning Trump would “destroy” the Republican party to being one of his most ardent allies, said Trump would pick Haley “if he thought it would help him win. But the longer [the primary] goes and the more scar tissue accumulates, the less likely it is”.

Asked if she would join Trump’s ticket, Haley has scorned the question – but not ruled it out.