Most of Mr. Trump’s aides ignored his changing story. But in January, shortly before his inauguration, Mr. Trump told a Republican senator that he wanted to investigate the recording that had him boasting about grabbing women’s genitals.
“We don’t think that was my voice,” Mr. Trump told the senator, according to a person familiar with the conversation. Since then, Mr. Trump has continued to suggest that the tape that nearly upended his campaign was not actually him, according to three people close to the president.