In an interview yesterday, Arpaio denied this.
But a source who asked to remain anonymous for this article says Arpaio believed it was possible he'd need to resign if re-elected, and had plans to back Arizona U.S. Marshal David Gonzales, a Republican, in a special election to replace him.
Of course, the longtime sheriff didn't win. He lost his bid for a seventh term in office last week to his Democratic opponent, Paul Penzone.
The primary reason for Arpaio's interest in resigning may have been his legal problems, the source says. Arpaio's under a criminal contempt charge in federal court for his failure to comply with a judge's orders in the long-running racial-profiling lawsuit, Ortega Melendres vs Arpaio.
"He knew this contempt charge was going to go on" if he'd been re-elected, the source says, and Arpaio believed that he might be able to make a deal that allowed him to retire without a "booking mug."
Arpaio's wife, Ava, was diagnosed with stomach cancer last year, and "he was going to use that as the reason" he resigned, the source says.
On the other hand, the sources says that Arpaio believed for weeks that it was possible that Trump would win and appoint him to a cabinet position or some other job, the source says. Although Arpaio complained that he "didn't want to go to D.C.," the source reports that the sheriff also said repeatedly that he didn't know how he could refuse Trump.
During the interview with New Times on Thursday, Arpaio initially denied the rumor that he would've resigned.
"You think I would raise $13 million, go through all the aggravation with everybody after me, to resign?" he said with typical bluster. "That's not me. That would never happen."
As he went into detail, it became clear that the source may not be entirely mistaken.
"Gonzales would like to be the sheriff, and I said, if something happens to me, okay, during the next four years, he could apply, put his name in, and I wouldn't oppose," Arpaio said.
What did he think would happen to him? New Times asked.
"If I get shot or something," he answered.
Gonzales, who was first appointed to his position by President George W. Bush in 2002, declined comment for this article. A lifelong Republican, Gonzales considered running for sheriff this year but decided against it, telling New Times in August that he didn't think anyone could beat Arpaio in a Republican primary.
Arpaio said he wouldn't have left office for a position in the Trump Administration.
He then spent approximately 15 minutes explaining how much he was "hooked" on Trump both professionally and personally, and that he didn't know how he could ever turn Trump down.
Not only do Arpaio and Trump see eye-to-eye on political issues like illegal immigration and abortion, but Trump has shown compassion for Ava, as Arpaio mentioned in July during his speech at the Republican National Committee's convention. On the day Trump announced his candidacy, Arpaio said he predicted Trump would be president.
"The reason I'm saying all this — what happens if he calls? How do you turn him down?" Arpaio said.
Arpaio seems to have hope that Trump may still hire him. Indeed, even after voters rejected a seventh term for Arpaio, and as the soon-to-be-former sheriff waits to learn his fate in federal criminal court, Trump's reportedly considering Arpaio for Homeland Security Secretary.
"The call — it may come at any time," Arpaio said.
But Arpaio said he won't chase after Trump for a job.
"I haven't got a call from him" about a position, Arpaio said. "I'm not gonna bother him. I could talk to him, but I'm not going to."
Arpaio claimed that he knows Stephen Bannon, Trump's controversial pick for chief-of-staff, "very well from way back."
"So I know all these guys in the administration," Arpaio said, adding that his appointment would be "all up to them."
Asked about his qualifications for the high-ranking position, Arpaio gave New Times his newly-update executive resume, which shows he served as sheriff from January 1993 to December 2016.
"I'm not bragging, but I think I'm pretty qualified," he said.