Arizona Gov. Doug Ducey (R) on Tuesday quietly met with Sen. John McCain John Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE (R) and his wife, Cindy, at the couple’s home outside Sedona, Ariz., GOP sources in the state told The Hill.

The meeting, which was not on the governor's official schedule, comes amid speculation over whom the Republican governor would appoint to fill the Senate seat should the ailing 81-year-old senior lawmaker and Vietnam War hero unexpectedly leave office.

McCain is undergoing treatment for an aggressive form of brain cancer known as glioblastoma and has remained in Arizona since mid-December.

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GOP sources with knowledge of the meeting Tuesday said they did not specifically know what was discussed or if the senator had explicitly told the governor who he prefers to succeed him in office.

Ducey spokesman Daniel Scarpinato confirmed to The Hill that the meeting in Cornville had occurred while pushing back at those who may read into it.

"John McCain is our senior senator. He and the governor work on a variety of issues together. Like others, the governor wanted to spend time with Senator McCain, and it was a great visit,” Scarpinato wrote in an email.

“To anyone who uses this as an opportunity to speculate or fan the rumor mill: Washington DC's obsession with this when there is no issue to be discussed is disgraceful," he continued. “John McCain is our senator until 2022, and the governor is looking forward to him returning to the U.S. Senate."

McCain spokeswoman Julie Tarallo also acknowledged the meeting and said Ducey's wife was present.

"Senator McCain and Cindy enjoyed a visit with Governor Doug Ducey and First Lady Angela Ducey in Cornville, Arizona, yesterday," Tarallo said in an email. "The McCains are grateful for the Ducey family’s longstanding friendship and support.”

The meeting took place before a key deadline in Arizona.

Under state law, Wednesday marks the final day that a vacancy for McCain's seat could trigger a special election before 2020. After Wednesday, Ducey will have the power to appoint someone to the Senate seat if it does become open.

McCain allies in Arizona and Washington have been pushing for Cindy McCain to be appointed to her husband's seat.

Former Arizona Attorney General Grant Woods (R), John McCain's close friend, and former Sen. Jon Kyl (R-Ariz.), McCain's old colleague, are two other names being tossed around in McCain circles.

“Ducey has always enjoyed, from the first time that he ran for office for state treasurer in 2010, a very respectful relationship with Sen. McCain,” one Arizona Republican source told The Hill.

“I can imagine the governor would entertain that this is a man, a hero, a patriot who deserves every consideration for a recommended appointment, whether that is Cindy McCain, Grant Woods or somebody else.”

Updated at 6:41 p.m.