Before his likely announcement, according to two people who have spoken with him, Mr. Walsh has hired a senior political adviser, organized meetings with high-profile Trump antagonists in New York City, and published an Op-Ed in The New York Times with the goal of previewing his campaign message…

“He lost me for good in Helsinki, when he stood in front of the world and said, ‘I believe Putin and I don’t believe my fellow Americans,’” Mr. Walsh said, framing a potential run as a moral imperative “to stick our necks out because when people see that, more and more people will.”

Mr. Walsh is being encouraged by William Kristol, the conservative writer and former editor of the now defunct magazine The Weekly Standard. Mr. Kristol has been a “Never Trump” Republican since Mr. Trump was elected in 2016 and has been working hard over the past year to recruit someone to run against him.

Mr. Kristol said Mr. Walsh’s comfort with the in-your-face format of conservative talk radio makes him a potentially more effective combatant against Mr. Trump than someone like William Weld, the genteel former governor of Massachusetts, whose own primary challenge to the president has gained little traction.