The Washington Post has not independently confirmed the account, which builds on a story published earlier this week by the Daily Beast reporting that Walker, who is campaigning on an antiabortion platform, paid for the woman to have an abortion.
Walker denied paying for an abortion and said he did not know what woman was making the allegation.
“I know nothing about any woman having an abortion,” Walker said Thursday to conservative radio host Hugh Hewitt.
The woman, who has not been publicly identified, has not responded to multiple inquiries from The Post.
Walker’s campaign did not immediately respond to a message seeking comment about the Times’s report.
The revelations threaten to further complicate one of the most competitive Senate campaigns in the country and confirm fears among some Republicans that Walker’s chaotic personal history, including allegations of domestic violence, will continue to attract attention and scrutiny in the final weeks of the campaign.
Also on Friday, Walker’s campaign fired a political director over accusations that he had unauthorized contacts with reporters, according to a person familiar with the events, who spoke on the condition of anonymity to discuss internal campaign matters.
Republicans have sought to go on offense in Georgia, releasing a new political advertisement that highlights Democratic Sen. Raphael G. Warnock’s history of opposition to abortion and other issues.
The candidates are set to debate next Friday.
Alice Crites and Michael Scherer contributed to this report.