Other potential pardon seekers and their allies are discussing a range of strategies to win over the president. They include highlighting donations to Mr. Trump, spending money at his properties, trying to hire lawyers or lobbyists seen as close to him and emphasizing business connections that could help Mr. Trump after he leaves office.

Mr. Gates, who received a 45-day jail sentence after cooperating with investigators, published a book last month accusing the special counsel’s team of using devious strong-arm tactics to pursue Mr. Trump and his allies. Mr. Gates conceded that his criticism of the investigation could potentially help with a pardon, but he added that “my motivation in writing the book was not to seek a pardon; it was to expose the truth about the Russia investigation.”…

Others seeking creative ways to forge ties to the president include Joseph Maldonado-Passage, the former Oklahoma zoo owner who is better known as Joe Exotic. His representatives have been running a carefully orchestrated campaign to try to persuade Mr. Trump to pardon Mr. Maldonado-Passage, who is one year into a 22-year sentence for trying to hire a hit man to kill an animal-rights activist.

They have focused on getting Mr. Trump’s attention through appeals to Donald Trump Jr. and Mr. Kushner, appearances on Fox News and a visit to the Trump International Hotel in Washington where, one organizer said, they ran up a tab of about $10,000 to try to get Mr. Trump’s attention.