Sen. Lisa Murkowski Lisa Ann MurkowskiClub for Growth to spend million in ads for Trump Supreme Court nominee Pebble Mine CEO resigns over secretly recorded comments about government officials Maryland's GOP governor says Republicans shouldn't rush SCOTUS vote before election MORE (R-Alaska) is not worried about a 2022 challenge from former Alaska Gov. Sarah Palin (R), who has suggested she could run for the Senate because of the incumbent’s opposition to Supreme Court Justice Brett Kavanaugh Brett Michael KavanaughHarris faces pivotal moment with Supreme Court battle Poll: 59 percent think president elected in November should name next Supreme Court justice Feinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight MORE.

“I don’t know the former governor’s interest in being involved in elected politics again and she’s really been out of the picture in the state for many years now,” Murkowski told The Hill.

“I don’t know whether this is just wishful thinking by some that would like to see me out so they’re looking for names,” she added.

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Fox News and conservative talk radio host Sean Hannity started the buzz over a possible Palin comeback.

“I tell you, the one person I'd love in Alaska to run against her would be Sarah Palin,” Hannity said on his radio show Tuesday. “Maybe Gov. Palin could make a political comeback. I think the people there would like that a lot.”

Murkowski was the only Republican to oppose Kavanaugh and voted against moving his nomination forward. She voted "present" in the final confirmation vote for Kavanaugh because her vote would not have changed the outcome and another GOP senator was absent.

Hannity on Tuesday also noted that the Alaska Republican Party is considering a reprimand of Murkowski for her opposition to Kavanaugh.

Palin, for her part, taunted Murkowski about a possible primary challenge after she voted to block the nominee on the Senate floor.

“Hey @LisaMurkowski — I can see 2022 from my house …” Palin tweeted, paraphrasing a line that was famously attributed to her in the 2008 presidential campaign, when she was GOP candidate John McCain John Sidney McCainThe Memo: Trump's strengths complicate election picture Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' Cindy McCain: Trump allegedly calling war dead 'losers' was 'pretty much' last straw before Biden endorsement MORE’s running mate.

Palin and Murkowski have long had a strained relationship.

Palin defeated the senator’s father, Frank Murkowski, who was the sitting governor at the time in the 2006 Republican primary.

The then-Alaska governor also backed Tea Party candidate Joe Miller when he defeated Murkowski in the 2010 Alaska Senate Republican primary.

Murkowski kept her seat by beating Miller in the general election with an extraordinary write-in campaign.

Since then, however, Murkowski’s political stock has risen while Palin’s has dropped off.

Murkowski scored a huge coup when she negotiated with Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) to include language in the 2017 tax-reform package opening up the Arctic National Wildlife Refuge (ANWR) to oil drilling.

Opening ANWR to energy exploration had been a top priority of her father, who served in the Senate from 1981 to 2002, and the legendary late Sen. Ted Stevens (R-Alaska).

President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE, however, warned this past week that Murkowski would pay a political price for opposing Kavanaugh.

“I think she will never recover from this,” Trump told The Washington Post. “I think the people from Alaska will never forgive her for what she did.”

Murkowski later told reporters she wasn’t too worried.

“I know Alaska's political terrain better than he does,” she said.

If Palin decides to run for the Senate, she will have to find a way to reconnect with Alaska voters.

She said last month that she and her husband are ready to leave the state and “get outside and do more.”

“We’re not going to be holed up in Wasilla, Alaska, the rest of our life,” she told the Daily Mail in an interview.

Palin has spent much of her time in Arizona in recent years. She sold her home in Scottsdale, Ariz., for $2.3 million in 2016.

An Arizona Republican official told The Hill that he thought the odds are slim that Palin would take on Murkowski.

And Murkowski said Hannity’s call for Palin to run against her in 2022 is merely a sign of frustration over her vote on Kavanaugh.

“This is a response from those who didn’t approve of my vote on Kavanaugh and so I understand that,” she said.

But Murkowski told reporters in an earlier interview that she was going to feel political blowback no matter how she voted.

“There has been support and there’s been opposition,” she said, characterizing the reaction of constituents after her vote against Kavanaugh.

“We are still receiving feedback from Alaskans. Some very, very supportive recognition and some who are disappointed,” she added. “On this one, Alaskans were pretty much split down the middle and so you knew going into it, you’re going to make half the people happy and half the people not happy.”

Despite her vote, she retains the vocal support of McConnell, who defended his colleague after Trump’s criticism.

“She’s certainly going to recover,” McConnell told The Associated Press in an interview. “She’s about as strong as you could possibly be in Alaska.

“Nobody’s gonna beat her. I’m proud she’s in the Republican conference,” he said.