Sen. Rand Paul Randal (Rand) Howard PaulGOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill Overnight Health Care: Senate Democrats block GOP relief bill | Democrats reveal Medicaid chief's spending on high-paid consultants | Trump calls question about why he 'lied' about COVID-19 a 'disgrace' MORE (R-Ky.) predicted on Wednesday that there isn't an "appetite" for a 2020 White House bid by incoming Sen. Mitt Romney Willard (Mitt) Mitt RomneyThe Memo: Warning signs flash for Trump on debates GOP votes to authorize subpoenas, depositions in Obama-era probe Overnight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' MORE (R-Utah), whose recent criticism of President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE is fueling talk of a potential primary challenge.

"I don't think there's an appetite for a Romney run within the Republican Party," Paul told reporters during a conference call on Wednesday, asked if Romney should "declare his intentions" for 2020.

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Romney is under criticism from Trump, conservative allies and even some of his soon-to-be colleagues for a sharply critical Washington Post op-ed where he claimed Trump “has not risen to the mantle” of the presidency.

Spencer Zwick, who established Romney’s donor network during his two previous presidential campaigns in 2008 and 2012, has been taking calls from donors encouraging Romney to run for the GOP presidential nomination in 2020, two people familiar with the discussions told The Washington Post.

But Paul added on Wednesday that, in addition to there being no "appetite" for Romney himself to run, he also didn't think a "Romney-type of establishment, big government Republicanism is really frankly popular enough to win a general election."

Romney, who has had a years-long on and off feud with Trump, told donors last year that he believed the president would "easily" win reelection in 2020.

“I think President Trump will be re-nominated by my party easily, and I think he’ll be reelected solidly,” Romney said at the time.

Paul, an ally of Trump's in the Senate, has been critical of Romney's op-ed. He tweeted earlier Wednesday that Romney is trying "to signal how virtuous he is." Paul is also scheduled to go on Fox News later Wednesday to discuss the issue.

He added during the press call with reporters that he believes Romney's criticism will be a "minority opinion" within the Senate GOP caucus, and that he didn't believe Trump "deserves to have a new senator coming in, attacking his character."

"I think this is bad for the Republican Party," Paul said. "[And] really bad for any kind of ability to work together in the Senate to get things done.”