DALLAS — Senate Majority Leader John Thune said Thursday he would be open to courting Sen. John Fetterman into the Republican conference, following the Pennsylvania Democrat’s unexpected virtual appearance at a GOP convention.

“If and when he is ready to have that conversation, we are certainly ready to have it,” Thune (R-SD) told The Post in an exclusive interview. He argued that Fetterman may find it “increasingly hard” to remain aligned with a Democratic Party he described as distant from the senator’s “core values,” adding that Fetterman’s remarks a day earlier appeared to underscore that divide.

Thune said he has not pressured Fetterman to make any move. “I don’t push him on it,” he said on the sidelines of the Republican midterm convention in Dallas, one day after Fetterman appeared by video on the event’s jumbotron to praise Pennsylvania Sen. Dave McCormick, a Republican.

The appearance drew sharp criticism from fellow Democrats. Rep. Madeleine Dean (D-Pa.) brushed off the video endorsement as a “stunt” and then criticized Fetterman’s “work ethic,” saying the senator was “just not present” in carrying out his official responsibilities.

“My constituents are livid. Those who went out and knocked doors for him are absolutely livid,” Dean said.

Fetterman’s praise for McCormick was notable given that the Republican was once viewed as a potential 2022 Senate rival. The moment came as speculation continues over whether Fetterman could eventually change his party registration — or face a serious Democratic primary challenge down the road.

Rep. Chris DeLuzio (D-Pa.), another Pennsylvania Democrat, has said he has “gotten a lot of encouragement” to challenge Fetterman in a 2028 primary.

Fetterman has already broken with Democrats on several high-profile issues, including key government funding votes. He has also suggested that if the Democratic Party formally becomes “the anti-Israel party,” he would be forced to leave it.

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“I’d be a terrible Republican who still votes overwhelmingly with Democrats,” he has also said, referring to a voting record that shows at least 80% of the time he joins with his own caucus.

“I’m a lifelong Democrat who votes overwhelmingly with my party — and should the Senate flip in November, I will still be the 51st vote that I ran on,” Fetterman clarified later in a statement.

The cross-party endorsement isn’t without precedent. Former independent Sen. Joe Lieberman, who caucused with Democrats, did the same for his longtime friend Sen. John McCain (R-Ariz.) at the 2008 GOP convention.

Four years before that, Sen. Zell Miller (D-Ga.) also backed then-presidential nominee George W. Bush at the Republican National Convention.

In Wednesday’s video appearance, Fetterman called himself a “common sense Democrat” and expressed willingness to work across the aisle with McCormick — and President Trump — to deliver for steel workers and other Pennsylvanians.

“I’m always going to reject the extremes and socialism and that anti-American way of life,” he also said.

More Republicans have a favorable view of Fetterman than McCormick, an August survey conducted by The New York Times, The Philadelphia Inquirer and Siena University found.

At least 73% of registered Republican voters expressed a positive opinion about Fetterman, while 63% did about McCormick.

Meanwhile, most registered Democratic voters (63%) have an unfavorable opinion of Fetterman, and 22% have a favorable view.