President Trump said Thursday that he would nominate Jovita Carranza, the United States treasurer, to lead the Small Business Administration, replacing the former pro wrestling executive Linda E. McMahon.

Ms. McMahon, the former chief executive of World Wrestling Entertainment, stepped down as the agency’s administrator last week. People familiar with Ms. McMahon’s thinking said she was expected to take a position at the America First PAC, a political action committee supporting Mr. Trump’s re-election, where she is expected to help raise money.

Mr. Trump announced the nomination of her successor in a tweet.