But even as Mr. Ryan was said to be reconsidering, his close associates cautioned that he had no intention of fighting for the job and would most likely accept it only by acclamation — including the support of the hard-line conservatives who pressed to oust Mr. Boehner and helped drive the majority leader, Kevin McCarthy of California, out of the speaker’s race on Thursday.

“If the conference decides as a whole that they want him to do it, it is possible,” said a Republican official close to Mr. Ryan who asked not to be identified because he was not authorized to speak publicly. “If there are still those guys who are holding out trying to make a point, it is not going to happen.”…

Mr. Fleming noted that the Freedom Caucus, which has about 40 members, previously announced its support for Representative Daniel Webster, a little-known lawmaker from Florida, and would stick with him until other candidates emerged and could be interviewed by the group.

“Remember, for us much of it has to do with the process and empowering individual members and the constituents that sent us here,” Mr. Fleming said. “So it’s not always about the personality.”