PHOENIX — Ambitious Republicans anxious for a shot at a U.S. Senate seat have begun quietly jockeying to be appointed as the successor to Sen. John McCain John Sidney McCainAnalysis: Biden victory, Democratic sweep would bring biggest boost to economy The Memo: Trump's strengths complicate election picture Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R), even as he battles an aggressive form of brain cancer.

The lobbying campaigns, described to The Hill by half a dozen GOP strategists and aides, have angered many Republicans, who see any public chatter as disrespectful to a senator who has helped shape modern Arizona.

Chief among those upset is the man who would make an appointment, Gov. Doug Ducey (R), who issued a brushback pitch during a radio appearance last week.

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“I have found it a little bit off color, some of the prognosticators and pundits who have been making these predictions as to the senator's outcome. I think people should be praying for him and rooting for him,” Ducey told KTAR radio. “To the politicians out there that have been openly lobbying for this position, they've basically disqualified themselves by showing their true character.”

Observers in Phoenix interpreted Ducey’s comments as a shot at three politicians who have been open about their interest in a Senate seat: Rep. Paul Gosar Paul Anthony GosarPelosi must go — the House is in dire need of new leadership LWCF modernization: Restoring the promise Trump tweets his people have all left Drudge MORE (R), former state Sen. Kelli Ward (R) and former Rep. Matt Salmon Matthew (Matt) James SalmonCOVID-19's class divide creates new political risks Arizona voters like Kyl but few think he'll stick around Former Sen. Jon Kyl to replace McCain in Senate MORE (R).

Gosar’s interest in serving in the Senate is hardly concealed, Republican operatives said.

He conducted polling measuring his standing in the race to replace retiring Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R) earlier this year, and his chief of staff has emailed a member of Ducey's staff about McCain's seat, according to three sources with knowledge of the conversation.

“At this time my prayers are with Sen. McCain. There will be a time and a place for any political discussion in due course,” Gosar said in a statement to The Hill.

Ward, who challenged McCain in the 2016 Republican primary, said shortly after McCain was diagnosed with cancer that he should resign — and that she should be considered to replace him.

“We are laser focused is on winning Jeff Flake’s seat, which we are in prime position to do,” said Ed Rollins, Ward's campaign chairman. “If a situation arises where an appointment is needed, the governor should appoint another strong conservative, who can partner with Dr. Ward after she wins.”

Salmon, who is now the top lobbyist at Arizona State University, has made his interest in the seat known, though more tactfully than the others. Salmon had lunch with Ducey's chief of staff earlier this month — something his allies made known among top Republicans around the capital — though a source close to the former congressman said the appointment did not come up.

“He has an interest in serving in the Senate, yes, but he has no interest in lobbying for a vacancy that doesn't exist,” the source close to Salmon said. “He feels he has absolutely no role in that decision anyway.”

Former Rep. John Shadegg (R) is also said to be on the list of candidates who would be considered to fill a vacancy. McCain is close to Grant Woods, his chief of staff when McCain served in the House and later a two-term attorney general.

Shadegg did not respond to an email, and Woods could not be reached during the holidays.

After a health scare two weeks ago, McCain returned home to Arizona to spend the holidays with his family. He tweeted on Dec. 18 that he was “looking forward to returning to work after the holidays.”

McCain's spokeswoman declined to comment for this story. A spokesman in Ducey's office, too, declined to comment.

Several Republicans who have seen McCain lately say he remains in a wheelchair, a side effect of the treatment regimen he is undergoing, and that he is still engaged on issues that matter to him.

Cindy McCain is giving Ducey's office and Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE’s (R-Ky.) office regular updates on her husband's progress, those Republicans said.

Arizona is already a key battleground in the war for control of the Senate. Flake's decision to retire, after polls showed him trailing Ward in the GOP primary, have given Democrats their best opportunity to compete for a Senate seat in the state since Dennis DeConcini retired in 1994. Even Republican stalwarts see Rep. Kyrsten Sinema (D) as a strong contender.

Ward, who met with President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE last week at his Mar-a-Lago estate, remains the Republican front-runner. She is likely to face a challenge from Rep. Martha McSally Martha Elizabeth McSallyThe Hill's Campaign Report: Presidential polls tighten weeks out from Election Day Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' New ABC/WaPost poll finds Trump edging Biden in Arizona, Florida MORE (R), who has told colleagues she will run but who has yet to make her bid official. In an interview last week, McConnell called McSally one of his top recruits.

Arizona state law allows the governor to appoint a replacement if a Senate seat becomes vacant. If the vacancy occurs at least six months before the next general election, voters would pick a candidate to fill the remainder of the unexpired term. That means Arizona could have two Senate seats on the ballot in November, a prospect some Republicans fear as political winds appear to shift toward Democrats.