Sen. Ted Cruz, R-Texas, says he is not interested right now in serving on the U.S. Supreme Court. He “reveres the institution,” Cruz says, but prefers to stay engaged in politics.

“I don’t want to stay out of political and policy fights,” Cruz told The Hill news organization Wednesday. “I want to be right in the middle of them. The Senate is the battleground for just about every big policy fight right now.”

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Cruz is running for reelection in Texas. He faces Rep. Robert “Beto” O’Rourke, D-Texas, in the November election.

Cruz’s name has frequently been mentioned in connection with the Supreme Court, though.

After graduating from Harvard Law School, he clerked for Judge J. Michael Luttig on the 4th U.S. Circuit Court of Appeals—a Supreme Court training ground during the George W. Bush administration—as well as for then-Chief Justice William Rehnquist.

Cruz went on to practice at Cooper & Kirk, PLLC, an elite conservative litigation boutique, and the U.S. Justice Department. On leaving Washington, he became solicitor general of Texas, representing the state in all appeals court matters.

Cruz has argued nine cases before the Supreme Court.

One of Cruz’s closest congressional allies, Sen. Mike Lee, R-Utah, appears on President Donald Trump’s list of possible Supreme Court nominees. Lee also practiced law before his election to the Senate and clerked for Justice Samuel Alito. His brother, Utah Supreme Court Justice Thomas Lee, is also a contender for the next high court nomination.

Speculation abounds in Washington about the future of Justice Anthony Kennedy, the 81-year-old anchoring the high court’s center. Some observers speculate that the court’s recent actions and thin docket for the coming term suggest a retirement is imminent. The justice himself has been cagey as to his plans.

Recent Supreme Court retirements have been announced in April and May, suggesting that Kennedy already would have made clear his intentions were he actually departing. Still, the justice will remain under close scrutiny until the court adjourns at the end of June.

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