For his part, the Duke is selling the Verbier ski chalet he bought with the Duchess of York, his ex-wife, in 2014 as a "family investment" with a mortgage and private funding from the Queen.
The couple put the property on the market when they were sued by its previous owner, French socialite Isabelle de Rouvre, who alleged that they owed her £6.7 million from the £16.6 million sale.
De Rouvre, the former wife of Cyril Bourlon de Rouvre, the former French politician and Formula One tycoon, launched legal action in Switzerland in 2020 after they missed a deadline for a payment.
However, de Rouvre has now dropped her lawsuit and is thought to have been paid the outstanding debt, although it is unclear how the Duke and Duchess sourced the funds.
It means when the sale eventually goes through and other debts are paid, they will have a small profit to put towards a potential settlement which would be billed as a means of protecting the Royal family from further reputational damage.
On Friday, the Duchess returned home from a skiing holiday at the seven-bedroom chalet with her daughters, Princess Beatrice and Princess Eugenie, their respective husbands and babies.
Approached by a journalist at Geneva Airport, she declined to discuss the Duke's legal case, but said: "Onwards and upwards."
The Duke has so far indicated he wants to fight the allegations and clear his name.
However, if he does opt to offer Giuffre a payoff, which is likely to be in the millions, the Queen would be asked to contribute, alongside his own input, The Telegraph understands.
However, any potential deal would include a "no admission of fault or liability" clause as well as a non-disclosure agreement, preventing either party from discussing the settlement or the case in public, sources suggest.
The settlement issue has gathered traction in recent days as the Duke awaits a critical ruling from Judge Lewis Kaplan on his motion to have the civil case dismissed.
Andrew Brettler, his lawyer, argued that Giuffre had "waived her rights" to sue him when she entered into a $500,000 (NZ$737,500) release agreement with Epstein in 2009.
However, Judge Kaplan rejected most of Brettler's points and legal experts said it appeared "unlikely" that he would find in the Duke's favour.
The next stage would be an "intrusive" discovery and deposition process, in which the Duke is interviewed under oath by Giuffre's lawyers.
He will also be asked to hand over correspondence, phone logs, emails and diaries and those closest to him could be asked to testify.
While a settlement would stop the case from progressing further, it would have to involve Giuffre's co-operation.
However, both she and her legal team are understood to be determined to push towards a trial in the interests of seeking justice.
Giuffre has made clear that she wants to send a message that anyone accused of preying on young girls will face the full force of the law.
Taking money from the Duke, who she claims sexually abused her on three separate occasions, would not "advance that message" and could also trigger a public backlash.
Buckingham Palace declined to comment on the monarch's involvement.
