Prince Andrew will host a reception of business people at the World Economic Forum in Davos, Switzerland, on Thursday evening.
Virginia Roberts's lawyers have repeated the claims in documents given to a court in Florida.
Prince Andrew has categorically rejected any suggestion of wrongdoing.
BBC royal correspondent Peter Hunt says Prince Andrew will attempt to demonstrate he has not been too damaged by recent events when he appears.
The duke will speak and may make reference to the allegations and denials that have been issued but if he does any comments will be brief, our correspondent added.
Virginia Roberts, who is referred to in the case as Jane Doe #3, alleges she was forced by financier Jeffrey Epstein, a convicted sex offender, to have sex with Prince Andrew.
It is the first time Ms Roberts has given a statement in her own words to the courts.
Her lawyers said they had sent Prince Andrew a letter asking him to respond under oath to the allegations.
They say the letter was sent back to them as having been refused by the recipient.
The allegations against Prince Andrew emerged in evidence submitted to a US court in a case involving Epstein, who spent time in jail in 2008-9 for a sex offence with a minor.
Prince Andrew, 54 and fifth in line to the throne, stepped down as UK trade envoy in July 2011 following controversy over his then friendship with Epstein.
The prince is not facing any legal proceedings over the claims made in the US case.
The Duke of York is due to make his first public appearance since a US woman alleged she was forced to have sex with him when she was 17.