Two people familiar with the process say the White House is considering Republican Gov. Brian Sandoval of Nevada as one of several potential nominees to the Supreme Court.

The nomination of a Republican to fill a Supreme Court seat left vacant by the death of Antonin Scalia would be seen as an attempt by President Barack Obama to court the Senate GOP.

Sandoval, a former federal judge, met with Senate Democratic Leader Harry Reid on Monday for about 30 minutes, and Reid asked him whether he would be interested in being considered for the high court job, according to the source.

"He said he was interested," the source said of Sandoval, adding that "a number of people are being checked out" for the job.

​The officials declined to be named because they weren't authorized to speak publicly.

USA-RANCHERS/NEVADA

Sandoval greets ranching families at the Nevada state capitol on May 30, 2014. (Max Whittaker/Reuters)

As governor, Sandoval has taken a traditional Republican stance in support of gun rights, but his more moderate views on social issues, such as abortion rights, could make him an attractive choice for the Democratic president.

A 52-year-old Mexican-American, Sandoval was appointed a judge by Republican George W. Bush, Obama's predecessor, before being elected governor in 2010. He abandoned his state's legal defence of a same-sex marriage ban before the Supreme Court declared such bans unconstitutional last year.

The governor said over the weekend he was honoured his name was mentioned but had heard nothing to think the Democratic president is considering him.

White House spokesman Josh Earnest declined during a briefing to confirm whether Sandoval was on Obama's list of potential nominees.

Republicans oppose Obama nominations

The Senate must confirm any high court nominee.

Senate Majority Leader Mitch McConnell announced on Tuesday that the Senate will not hold hearings or vote on any Supreme Court nominee until after the next president takes office in January.

After word emerged of Sandoval's possible appointment, McConnell was adamant that no one would be confirmed until a Nov. 8 general election determines who succeeds Obama. Republicans are hoping to win back the White House.

McConnell remained unswayed even with word that Obama was considering a Republican for the job.

"This nomination will be determined by whoever wins the presidency in the fall," McConnell said.

With files from Reuters