“It’s highly likely that there is a sweetheart deal there, and it is a very good thing with almost no downside,” said Tom O’Halloran, host of the Texas-based conservative webcast Patriot Radio Show, who subscribes to the theory of a secret Trump-Cruz ticket.

“It’s a brilliant move,” he said. “It sounds to me like a deal that was made in heaven.”

Mr. O’Halloran and other believers pointed to a purported secret meeting between Mr. Trump and Mr. Cruz in Dallas at the end of the summer and the absence of attacks waged by the combative Mr. Trump against Mr. Cruz, the only major candidate to be spared Mr. Trump’s blisteringly personal attacks.