Rep. Cathy McMorris Rodgers Cathy McMorris RodgersHillicon Valley: Trump backs potential Microsoft, TikTok deal, sets September deadline | House Republicans request classified TikTok briefing | Facebook labels manipulated Pelosi video Top House Republicans request classified TikTok briefing More than 100 lawmakers urge IRS to resolve stimulus payment issues MORE (R-Wash.), a member of House GOP leadership, is not ruling out supporting Rep. Jim Jordan James (Jim) Daniel JordanHouse panel pulls Powell into partisan battles over pandemic Sunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election House passes resolution condemning anti-Asian discrimination relating to coronavirus MORE (R-Ohio) in his bid for Speaker.

"I am staying open. I have not made a commitment for who I will be supporting for leadership," McMorris Rodgers told the local newspaper Inlander this week when asked if she would support Jordan.

"I really believe that it's premature for us to be jockeying for leadership positions when we need to focus on our races,” the House GOP caucus chair added.

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Jordan launched a bid last month to replace retiring Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.), setting up a battle with House Majority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy says there will be a peaceful transition if Biden wins GOP lawmakers distance themselves from Trump comments on transfer of power McCarthy claims protests in Louisville, other cities are 'planned, orchestrated events' MORE (R-Calif.).

Ryan in April threw his support behind McCarthy, his deputy, to be his successor. Ryan told NBC News at the time, "We all think that Kevin is the right person."

A Politico/Morning Consult poll of registered voters released earlier this month showed slightly higher support for Rep. Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.), who is currently the No. 3 House Republican, to become Speaker over Jordan and McCarthy.

The Speaker is decided among lawmakers when the new Congress convenes, and many members have pushed to hold off on the leadership battle until after the November midterm elections as Republicans seek to defend their House majority.

Jordan’s bid for Speaker has been mired in controversy in recent weeks since former wrestlers at The Ohio State University (OSU) alleged that he ignored reports of sexual abuse when he was a coach there years ago.

“Jordan definitely knew that these things were happening — yes, most definitely. It was there. He knew about it because it was an everyday occurrence,” former wrestler David Range said.

Jordan has denied the claims, calling the timing of the allegations “suspect.” Multiple former wrestlers from the school have also come out in defense of Jordan.