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News veterans Shepard Smith, Steve Kornacki and Joy Reid are all on the shortlist to take over Chris Matthews’ abruptly vacated seat on MSNBC’s “Hardball,” sources told The Post.

The legendary political journalist surprised viewers Monday when he abruptly announced his retirement in the wake of accusations that he acted inappropriately toward a female guest, leaving Kornacki, a national political correspondent, to fill in.

In addition to Kornacki, who is known for giving analysis of polls and election results, network brass are thinking of giving “Hardball” to Reid, who hosts MSNBC’s popular weekend show “AM Joy.”

Reid frequently substitutes for other MSNBC hosts, including Chris Hayes and Rachel Maddow.

Meanwhile, Smith, who quit his Fox News show “Shepard Smith Reporting” in October, is preparing for a return to TV in the summer and is also being considered, sources said.

The “Hardball” 7 p.m. slot is a tricky one to fill, according to a senior news TV source.

For more on Chris Matthews’ exit from MSNBC, listen to this episode of the Page Six podcast, “We Hear“:

“It comes straight after the evening news, when viewers want anchors to weigh in with their own thoughts and analysis — not just read the headlines, so it’s a tough gig,” the source said.

Smith has been off air since asking Fox to cut him from his contract so he could start “a new chapter,” saying: “After requesting that I stay, they graciously obliged.”

His exit came after he had signed a new, multi-year contract extending his role with Fox in 2018, according to reports.

Matthews abruptly retired from his longtime role as host of “Hardball” on Monday night following an allegation that he “inappropriately flirted” with a female guest.

The MSNBC anchor shared the shocking news at the start of his show, announcing on air, “I want to start with my headline tonight: I’m retiring.”

“This is the last ‘Hardball’ on MSNBC and obviously this isn’t for a lack of interest in politics,” he added.

An MSNBC insider told The Post that network executive Phil Griffin told Matthews this weekend in Washington, DC, where “Hardball” is filmed, that “he had to resign or retire immediately.”

“The news was kept a secret at the network until around 6 p.m. on Monday when all the senior staff were informed Matthews would retire at the top of his show, at 7 p.m.,” the insider said.

Matthews said he was leaving his post to make way for “younger generations” who are “improving the workplace.”

Kornacki took over Monday night’s show after a commercial break and gave a heartfelt tribute to Mathews.

“He knew the dark side of politics just like we all do,” Kornacki said. “He knew about the ugly and unflattering aspects of humanity that politics can bring out and even reward, the things that rightly turn off so many Americans to all of it.

“But Chris could see something beyond that, he could see the possibility that politics could also be used for something noble, even amidst all that human frailty.”

On Friday, freelance journalist Laura Bassett published a column in GQ, accusing Matthews of making inappropriate advances toward her twice as she readied herself to appear on his show.

Bassett’s allegations were just the latest in a series of setbacks suffered by Matthews.

While covering President Trump’s South Carolina rally last Friday, he mistook Jaime Harrison, a Democratic Senate candidate whom he was interviewing, for Republican Sen. Tim Scott. Both Scott and Harrison are black.

Matthews was slammed by progressives after last Tuesday’s Democratic presidential debate for asking Sen. Elizabeth Warren why she believed a woman who accused Michael Bloomberg of telling her to have an abortion while working at his company.

Days earlier, Matthews was widely criticized for comparing Sen. Bernie Sanders’ Nevada caucus win with Nazi Germany’s defeat of France in 1940.

He later apologized, calling the comparison a “bad” analogy.

Another MSNBC insider said Matthews’ recent gaffes contributed to his sudden departure.

“Chris was already on his way out because of his comments about Sanders, and his interview with Elizabeth Warren,” the network insider said.

“NBC and MSNBC will not tolerate any inappropriate behavior.”

An MSNBC spokesperson declined to comment.