Wyoming Republican Sen. John Barrasso will not say whether he’ll run for Senate Minority Leader Mitch McConnell’s position next year.

As the Senate Republican Conference chair, he is widely speculated to run.

“That election doesn’t occur until later in November. To me, the key election is the one earlier in November. The election for President of the United States and Senate seats all around the country,” Barrasso said at a news conference supporting Arizona Senate candidate Kari Lake in Phoenix on Thursday afternoon.

“And that’s why I’m here, that’s the election I’m concerned about,” he added.

McConnell, from Kentucky, has served as both minority and majority leader since taking office in 1985.

Texas Sen. John Cornyn announced that he’s entering the race to be his successor as the Republican Party’s Senate leader. South Dakota Sen. John Thune and Florida Sen. Rick Scott are also expected to jump into the race. Former President Donald Trump is also reportedly urging Montana Sen. Steve Daines to consider a bid as well, according to Politico.

Lake’s press conference primarily focused on the death of 22-year-old Laken Riley, who was killed by a migrant who crossed into the United States illegally. Barrasso and Lake placed the blame onto the Biden administration for migrant-related crimes. Both also emphasized their desire to have a majority in the Senate, maintain the House majority, and former President Donald Trump back in the White House to no longer face a divided federal government.