Mitt Romney met this week with William Kristol, who is pushing for a third-party alternative to Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE and Hillary Clinton Hillary Diane Rodham ClintonWhat Senate Republicans have said about election-year Supreme Court vacancies Bipartisan praise pours in after Ginsburg's death Trump carries on with rally, unaware of Ginsburg's death MORE.

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“He came pretty close to being elected president so I thought he may consider doing it, especially since he has been very forthright in explaining why Donald Trump and Hillary Clinton should not be president of the United States,” Kristol told the Washington Post Friday.

Kristol, editor of the conservative Weekly Standard, told the Post that he and Romney had met on Thursday in D.C.

And he said that even if Romney doesn't want to run himself, Kristol hopes he will support another third-party candidate.

“It was not like, ‘You should do it.’ I wouldn’t presume he’d do it. But I’m hoping that he begins to think about it a little more,” Kristol said. “His name is one of the names part of the discussion.”

Romney said Thursday at an event after the meeting that he would not vote for Trump, now the presumptive nominee, or Clinton.

“I don’t intend on support either of the major party candidates at this point,” he said, according to the Washington Examiner. And Romney plans to skip the convention this summer, along with many other prominent Republicans.

Romney reappeared in the political spotlight earlier this year to bash Trump, calling him "phony" and "a fraud," and was supportive of both Marco Rubio Marco Antonio RubioFlorida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Intelligence chief says Congress will get some in-person election security briefings MORE and John Kasich in their respective home-state primaries.