The names of a few well-known conservatives have been offered up in recent days as potential third-party standard-bearers, and William Kristol, editor of The Weekly Standard, has circulated a memo to a small number of conservative allies detailing the process by which an independent candidate could get on general-election ballots across the country.

Among the recruits under discussion are Tom Coburn, a former Oklahoma senator who has told associates that he would be open to running, and Rick Perry, the former Texas governor who was suggested as a possible third-party candidate at a meeting of conservative activists on Thursday in Washington.

Mr. Coburn, who left the Senate early last year to receive treatment for cancer, said in an interview that Mr. Trump “needs to be stopped” and that he expected to back an independent candidate against him. He said he had little appetite for a campaign of his own, but did not flatly rule one out.

“I’m going to support that person,” Mr. Coburn said, “and I don’t expect that person to be me.”

Trump opponents convened a series of war councils last week to pinpoint his biggest vulnerabilities and consider whether to endorse one of his two remaining opponents, Senator Ted Cruz of Texas and Gov. John Kasich of Ohio.