Ms Giuffre alleges she was sexually abused by the Duke of York, on three separate occasions, when aged just 17. She claims convicted sex offender Jeffrey Epstein coerced her into having sex with Prince Andrew in London, New York and on a Caribbean island.
She is suing him for damages in a New York court.
Andrew has strongly denied all the allegations against him.
On Friday the Prince’s lawyers finally accepted they had been served with legal papers, following several days of confusion.
They have until October 29 to respond to the claims on behalf of the Prince.
A source said Andrew’s team is preparing to challenge the claims against him more directly.
They told the Mail on Sunday: “The decision to bring in high-profile [US lawyer] Andrew Brettler to fight the civil case marks a significant turning point in approach.
“The US team will be looking to robustly engage and challenge the claims from Mrs Giuffre in a bid to provide the Duke with a platform to finally clear his name.
“They will be looking to examine and dismantle the claims one by one.”
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Nigel Cawthorne, author of ‘Prince Andrew: Epstein, Maxwell and The Palace’, is urging Andrew to give up his HRH title whilst the case is ongoing.
He commented: “Andrew is supposed to be an officer and a gentleman, so he should do the decent thing and give up his HRH title.
“Harry and Meghan had to stop using their HRH status and they haven’t been accused of anything.
“But in keeping his titles and his military roles, the Queen has been tainted by the accusations.”
In August 2019, Mr Epstein took his own live while awaiting trial on sex trafficking charges.
Earlier this week the Daily Mirror reported Andrew was holding “crisis talks” with his legal team.
A source told the newspaper: “The plan, if you can call it a plan, has been shambolic from the start.
“Now it’s all come to a head. He is extremely worried and the crisis talks are so he can get off the back foot. He knows he’s in a full-on crisis.
“The damage to his reputation is there for all to see but now he’s feeling the pressure from his family, though none of them have become directly involved.
“The whole thing’s a disaster.”