Several of the supporting actors in this year’s Republican primary are showing interest in the medium, too. Fred Thompson, the “Law & Order” star turned presidential candidate, will begin hosting a two-hour show in March, as the syndicator Westwood One is expected to announce this week. Mr. Thompson’s show would take the place of Mr. O’Reilly’s.

Rudolph W. Giuliani, the former mayor of New York City and a Republican presidential candidate, had been in negotiations with Westwood One for Mr. O’Reilly’s time slot, according to two people with knowledge of the talks who spoke on the condition of anonymity because a deal was not struck.