(CNN) Joe Arpaio, the controversial ex-Arizona sheriff convicted of criminal contempt, was preparing to go out to dinner with his wife on her birthday last August when he got a phone call from his lawyer. He said he would be coming by Arpaio's house with some papers that needed to be signed.

"He was playing cute," Arpaio recalled. When his lawyer arrived, he presented his client with pardon papers from the President of the United States.

In an interview with CNN, Arpaio insisted that he never asked Donald Trump for a pardon and never discussed the issue with him. The news, he said, was delivered abruptly with little formality: a single phone call with a White House lawyer "to see if I'd accept a pardon." And just like that, Arpaio's slate was wiped clean.

"Then the White House put out a press release," Arpaio said. "But I was not going to postpone the Italian dinner."

Arpaio took his wife to Arrivederci, where they ordered their favorites: spaghetti and meatballs and baked ziti. Throughout the meal, Arpaio was inundated with phone calls from reporters.

To this day, Arpaio -- a staunch supporter of the President for whom he campaigned for during the 2016 campaign -- says he can't be sure what prompted Trump to issue the first pardon of his presidency. But he does know when serious buzz about the possibility started: after a Fox News interview with Trump in Bedminster, New Jersey, last summer.

"A Fox reporter came up with that question and that sort of opened the door. People started talking about it," Arpaio said. Indeed, Trump said in that interview that he was "seriously considering a pardon" for Arpaio.

Like so many other aspects of the current presidency, Trump's wholly unconventional approach to pardons has puzzled Washington observers -- and has some people hoping to secure a pardon maneuvering to catch the President's eye.

"The media is the only way to send the message" to Trump, Simona Mangiante, wife of George Papadopoulos, told CNN. "I don't know how to reach him otherwise."

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The White House has already prepared paperwork to pardon dozens of people. And with special counsel Robert Mueller's investigation into collusion in the 2016 presidential election in high gear, there is also growing speculation about whether Trump will channel his executive power towards former aides and allies.

Speaking to reporters on Friday, Trump expressed regret that certain individuals associated with him -- including his former campaign chairman Paul Manafort and ex-national security adviser Michael Flynn -- have come under Mueller's scrutiny.

Trump has also teased the possibility clemency for celebrity businesswoman Martha Stewart and jailed ex-Illinois Gov. Rod Blagojevich -- comments that surprised both White House reporters and aides. One senior White House official said while Trump had floated both names privately, there had been no expectation that he planned to share them in public.

Trump then went a step further: He challenged NFL players (with whom he has fought about national anthem protests) and others to submit names of people unfairly treated by the justice system who deserved to be pardoned.

"If the athletes have friends of theirs or people they know about that have been unfairly treated by the system, let me know," Trump said.

There was nothing celebrity about Alice Marie Johnson, the grandmother whose sentence on a drug charge was commuted , but she had star power on her side. Reality TV star Kim Kardashian West took Johnson's case directly to the Oval Office.

Johnson's case wasn't the only time a pardon candidate had garnered Trump's attention through a high-profile figure. Sen. Ted Cruz, R-Texas, encouraged the President to pardon conservative activist Dinesh D'Souza, who pleaded guilty to making illegal campaign donations in 2014. Trump took Cruz's advice and pardoned D'Souza late last month

Still, plenty of other potential pardon candidates are reaching Trump through the conventional review process.

Another White House official said the Justice Department is recommending cases to the White House for consideration, as it would under any other administration. The Office of the Pardon Attorney at the Justice Department and Deputy Attorney General Rod Rosenstein sift through thousands of clemency applications to recommend either denials or pardons to the White House, the official said, and those recommendations are handed off to the White House counsel's office, led by Don McGahn.

McGahn's team then advises Trump on which course of action he should take, although the official said the "vast majority" of cases don't ultimately warrant a pardon or commutation.

For example, within the last three months, the Office of the Pardon Attorney notified a group of roughly 180 petitioners that they would not be receiving clemency from Trump, this White House official said.

Increasingly flexing his presidential muscle by granting more acts of clemency, Trump has alternated between such cases that reach his desk through the traditional Justice Department pipeline, and weighing celebrity pardon cases or cases brought to his attention by celebrities.

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Len Goodman, the lawyer representing Blagojevich, told CNN that he has "no way of knowing" why Trump said last week that he was "seriously thinking about" curtailing the ex-governor's jail time (Blagojevich is currently serving out a 14-year sentence).

"I have no way of knowing where it was coming from," Goodman told CNN about Trump's comments -- though he noted that Trump knows Blagojevich and met Blagojevich's family years ago. Blagojevich appeared on "The Celebrity Apprentice" in 2010.

Still, Goodman said he has taken no unusual steps to try to get Trump's attention. A clemency request for Blagojevich was filed "through the normal channels," he said, referring to the Justice Department, and there have been no meetings and discussions with anyone at the White House.

"We're just on pins and needles hoping that there would be some good news and that Trump will follow through," Goodman said.

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Cable TV gets results

Others are more than willing to try to catch the President's attention and make a direct appeal to him the best way they know how -- through cable television.

Papadopoulos's wife, Mangiante, has been pleading with Trump in recent TV interviews to pardon her husband. She said her husband, a former Trump campaign adviser who pleaded guilty to lying about his contacts with Russians and is now cooperating with Mueller, is "very stressed" and "has been hugely misunderstood."

Papadopoulos' lawyer has not yet formally filed a pardon petition with the Justice Department, Mangiante said, and that she has not been in touch with any members of the Trump administration to try to make a personal appeal because she doesn't know how. Going through the media is her best hope, she said.

It was a strategy that helped Kathleen Saucier, the mother of former Navy sailor Kristian Saucier who was charged with taking classified photos inside a submarine and sent to jail.

Kathleen Saucier had submitted a pardon request under President Barack Obama, and resubmitted the application when Trump came into office. She told CNN that there was a breakthrough of sorts when she was interviewed by Fox News' Sean Hannity.

"I remember someone sending me a text saying, 'Did you see President Trump talking about the kid on the submarine? Is that your son?'" Saucier said.

Kristian Saucier was pardoned by Trump last year.

The prospect of Trump wielding his pardon power in unconventional ways could have political implications.

Weeks before Trump pardoned Arpaio, he was approached about a potential pardon for Michael Grimm, the former New York congressman who pleaded guilty to tax fraud in 2014.

Grimm claimed during a debate this week that his opponent, Republican Rep. Dan Donovan, had privately asked Trump last year to pardon Grimm. The underlying suggestion was that it was a move to try to dissuade Grimm from running against Donovan. A source close to the Grimm campaign said Donovan personally told Grimm last summer that he had asked Trump to consider pardoning the ex-congressman, though Donovan did not explicitly suggest a "quid pro quo."

A spokeswoman for the Donovan campaign denied that Donovan, who is endorsed by Trump, ever pushed the President to look at pardoning Grimm. Instead, the spokeswoman said, Donovan merely mentioned to Trump that another Republican figure from the Staten Island area would soon be reaching out to request a pardon for Grimm.

A White House official said Grimm's claim "doesn't appear to be true" and declined further comment.