De Gea, who is with Spain's national team in France for the Euro 2016 tournament, told reporters Friday that the claims were "a lie and utterly false."
"I am the first to be shocked by the news. I want to deny any allegations," the goalkeeper said.
"They can publish whatever they want. It's all false. This gives me extra strength."
His comments were posted on the Spanish national team's verified Twitter account
and reported on its website.
De Gea spoke following Spanish newspaper El Diario's report of a witness account
in the trial against pornography entrepreneur Torbe.
Torbe -- real name Ignacio Allende Fernandez -- was arrested in April on multiple charges including sexual exploitation, child pornography and money laundering.
El Diario said the witness accused De Gea and Torbe of arranging for her and another woman to meet the other two footballers, who like De Gea were at the time also members of Spain's Under-21 team. It said the witness accused the two men of sexually assaulting the women at a hotel in Madrid.
CNN contacted the Spanish national team for comment but received no response Friday.
De Gea, 25, started his career with Atletico Madrid and made his senior debut in 2009.
Considered one of the world's best young goalkeepers, he was signed by English team Manchester United in 2011 and is still its first-choice after a move to Real Madrid fell through in August 2015.
He has represented his country nine times at senior level, and was a member of Spain's title-winning teams at the European U21 Championship in 2011 and 2013.
De Gea did not play at the 2014 World Cup in Brazil, but is vying with longtime No. 1 keeper Iker Casillas and Sergio Rico for a starting place at Euro 2016, which runs from June 10-July 10.
Host nation France kicked off the tournament Friday, while defending champion Spain's first game is against the Czech Republic on Monday in Toulouse.
"I am very calm. I am looking forward to practice and to continue enjoying what I love most," De Gea said Friday, adding that he heard about the news while in his hotel room.
"I told my family. They're calm because they know me."