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Nevada Gov. Brian Sandoval, a Republican and former federal judge, met with Sen. Harry Reid on Monday to discuss the open Supreme Court seat, according to multiple published reports.

The Washington Post said a knowledgeable source told the newspaper that the administration is vetting Sandoval, who is said to have told Reid, the Senate minority leader, at the meeting in Washington, D.C., that although he’s not sure he would accept a Supreme Court nomination, he wanted to remain a candidate.

In an interview with CNN, Reid, a Nevada Democrat, sang Sandoval’s praises.

"I don't pick the justices, but I know if he were picked, I would support the man," Reid said of the governor. "He's a good person, has a great record and has been a tremendously good governor in spite of having to deal with some very big problems there.”

Sandoval, who is 52, is considered to be a political moderate.

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Several media outlets said the governor’s office in Nevada either did not respond to requests for comment or said they had not been contacted by the White House regarding a nomination.

In an interview with the website The Morning Consult, Sandoval, who was in Washington over the weekend attending a governors' conference, said, “It would be a privilege” to be nominated. He said the Supreme Court “is the essence of justice in this country.”

Some political observers believe that if Pres. Barack Obama selected a Latino Republican to succeed Justice Antonin Scalia, who died suddenly earlier this month, on the Supreme Court, it would put Senate Republicans in a tight spot.

Senate Majority Leader Mitch McConnell, a Kentucky Republican, vowed not to allow confirmation hearings on anyone Obama might nominate. Senate Republicans want to hold off a Supreme Court selection until Obama leaves office in January.

Obama and his team are hoping to select a well-regarded candidate who Republicans would be hard-pressed to oppose, then build a public campaign of support for him or her, while ratcheting up political pressure on Republicans for standing in the way of a fair consideration.

Once Republicans are faced with an actual candidate instead of an "abstraction," Obama has said, opposition might soften. He told reporters last week that he hoped Judiciary Committee members would "recognize that it is their job to give this person a hearing" and then let their conscience dictate their vote.

Some Republicans have told media outlets that a Sandoval nomination would not affect their opposition.

But others said they would consider Sandoval, who was nominated to a district court post by George W. Bush in 2005. He quit four years later to run for governor.

The Associated Press contributed to this report.

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