Shortly after his victory last year, Donald J. Trump began revisiting one of his deepest public humiliations: the infamous “Access Hollywood” tape of him making vulgar comments about women.

Despite his public acknowledgment of the recording’s authenticity in the final days of the presidential campaign — and his hasty videotaped apology under pressure from his advisers — Mr. Trump as president-elect began raising the prospect with allies that it may not have been him on the tape after all.

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.