Trump could be about to name the most hawkish general in the U.S. military to be the nation’s next top counterterror official.

Gen. Paul Nakasone, the Army’s top intelligence officer, is set to be nominated as the new director of national intelligence, according to four people with knowledge of the discussions.

He is expected to replace Daniel Coats, the veteran intelligence official who has been at the agency for a dozen years.

Mr. Coats recently disclosed on Capitol Hill that Gen. John F. Kelly had been in “advanced discussions” to replace him, and the president has been discussing a new approach to counterterrorism for some time.

The officials said that the appointment of Gen. Nakasone, the current intelligence chief for U.S. Forces in Europe, who retired from the Army in 2014, would likely be unveiled at Mr. Trump’s second meeting with Russian President Vladimir Putin at the United Nations this week.

The news that Mr. Coats had been in “advanced discussions” about a job far above his current pay grade was reported Monday by The Washington Post.

In recent years, Gen. Nakasone has played a prominent role in Mr. Trump’s strategic outreach to Russia and had advised the president and his son-in-law, Jared Kushner, on his so-called pivot to the Asia Pacific.

Sources said that the general has often sided with Mr. Kushner when it comes to Russian foreign policy, including agreeing that Russia should be brought to heel in Syria.

Although Gen. Nakasone had been expected to be nominated to replace Mr. Coats, it was unclear for some time whether he would join the president in his current top job, a highly prestigious and high-level position that the president described as one of the most important jobs in U.S. government.

Michael Anton, a State Department spokesman, said on Twitter that the news of Mr. Coats’ possible departure had “gotcha reporting I don’t want to be involved in.”

He added: “CIA Director Pompeo, Ambassador Haley, DHS Secretary Kelly all deserving of high office.”