The Guardian reported that Amy Dorris told the paper in an interview that Trump assaulted her outside a bathroom in his VIP box at the tournament that year. She was 24 at the time, the newspaper said.
"He just shoved his tongue down my throat and I was pushing him off. And then that's when his grip became tighter and his hands were very gropey and all over my butt, my breasts, my back, everything," the newspaper quoted Dorris as saying.
The president's re-election campaign on Thursday said the allegations were not true.
"The allegations are totally false. We will consider every legal means available to hold The Guardian accountable for its malicious publication of this unsubstantiated story," said Jenna Ellis, a legal advisor to Trump's campaign.
Efforts to reach Dorris by phone for comment were unsuccessful.
The Guardian said in an email it stood by its reporting.
The newspaper published photos that it said were provided by Dorris showing her with Trump and said that it interviewed several people who Dorris confided in at the time of the incident. It said that in total she provided six photos showing the two together as well as her ticket to the tournament on the day she said the incident occurred.
Trump has faced a number of allegations of sexual misconduct prior to his time in office. Shortly before the November 2016 election an "Access Hollywood" recording from 2005 revealed him boasting about groping women. Trump dismissed the comments as "locker room banter" and apologized.
Dorris, a mother of twins, told the newspaper she considered coming forward in 2016 but decided against doing so partly out of fears for her family.
"Now I feel like my girls are about to turn 13 years old and I want them to know that you don't let anybody do anything to you that you don't want," she said.
