Mr. Trump often wants to find people with impressive résumés to fill out his West Wing, and Mr. Cohn — a former top executive at Goldman Sachs — was a key example of that kind of hire. But Mr. Trump’s advisers recognize that they are unlikely to draw another top executive and had been looking to hire from inside the West Wing.
Mr. Kudlow had been publicly critical of Mr. Trump’s push for stiff and sweeping tariffs on steel and aluminum imports.
But Stephen Moore, a friend of Mr. Kudlow’s and a fellow campaign adviser to Mr. Trump, said Monday that the administration’s tweaks to its tariff plan — such as providing country exclusions — had made it significantly more palatable to Mr. Kudlow.
When Mr. Trump said this month he planned to impose tariffs on imported steel and aluminum from every foreign country, Mr. Kudlow, along with Mr. Moore and the economist Arthur Laffer, wrote a critical column urging the president to reconsider. “Trump should also examine the historical record on tariffs,” they wrote, “because they have almost never worked as intended and almost always deliver an unhappy ending.”
Mr. Trump went ahead with the tariffs, but he signaled some countries, such as Mexico and Canada, could be exempt from them. Mr. Moore said that change was important.
“Larry, I think, will be supportive” of more tailored tariffs, he said. “My own hope is, if Larry gets this job, he can have an impact in pushing Trump in a good direction on this.”
Mr. Moore said that Mr. Kudlow would serve Mr. Trump well as a salesman for his economic agenda, including tax cuts and deregulation, and that his history with Mr. Trump was a factor in his consideration.
“I think Trump values Larry’s contributions to the campaign,” said Mr. Moore, a senior fellow at the Heritage Foundation. “Larry gave Trump a lot of legitimacy early on, with conservatives. Larry’s just a great communicator on the economy, and that’s what Trump needs.”
Heading into the weekend, the top contender to replace Mr. Cohn was Christopher Liddell, who is a special assistant to the president working with the Office of American Innovation on a team led by Jared Kushner, Mr. Trump’s son-in-law and senior adviser. Mr. Liddell’s previous experience as a chief financial officer for Microsoft had been seen as a selling point.
But after The New York Times reported that Mr. Liddell was under consideration, Mr. Trump received pushback from people both inside and outside the White House, according to the people close to the president. On Monday, The Wall Street Journal’s editorial board wrote a piece critical of Mr. Liddell’s views on free trade.
On Sunday, Mr. Trump again began discussing Mr. Kudlow as an option, the people close to the president said. On Monday, his advisers said he was leaning toward Mr. Kudlow, but stressed that the mercurial president is hard to predict and could change his mind several times.
Mr. Kudlow, if chosen, would be the rare revival in Mr. Trump’s circle — he criticized the president after the emergence of the “Access Hollywood” tape in October 2016. He later re-endorsed him, but Mr. Trump, who nurses grudges, was angry for some time, according to people close to him.
Mr. Kudlow is a CNBC commentator and radio host and a former Wall Street economist. He is a disciple of Mr. Laffer, the godfather of supply-side tax cuts, whom Mr. Kudlow credits for helping him overcome an alcohol- and substance-abuse problem more than 25 years ago. During the campaign and throughout Mr. Trump’s first year in the White House, Mr. Kudlow urged the president to go big with his tax-cut plan.
After Republicans pushed the $1.5 trillion cut through Congress late last year, Mr. Kudlow praised it effusively, predicting it would usher in annual growth of 3 percent to 4 percent on a long-run basis — a more optimistic assessment than most independent economists have offered — and would boost Republicans in this year’s midterm elections.
“Trump and the G.O.P. are on the side of the growth angels with the passage of powerful tax-cut legislation to boost business investment, wages and take-home family pay,” Mr. Kudlow wrote in December. “The Democrats, meanwhile, are left with stale class-warfare slogans about tax cuts for the rich.”