Sacoolas, who returned to the US after being charged with death by dangerous driving, said she would be willing to meet with Dunn's family.
Lawyers for alleged killer of 19-year-old motorcyclist issue public statement.
Anne Sacoolas returned to the US after the 19-year-old's death last year.
Anne Sacoolas, 42, was charged with causing death by dangerous driving in December, but the US rejected an extradition request.
Boris Johnson admits relationship may be "imbalanced" in response to claims Harry Dunn's alleged killer worked for American security services.
The family has called for a "full public enquiry into who knew what and when".
Lawyers For Harry Dunn And Epstein Victims Call For Exchange Of Road Death Suspect And Prince Andrew
The pair are calling for Anne Sacoolas to return to the UK and the Duke of York – who has not been summoned by police – to face questioning from the FBI in the US.
The 19-year-old was killed when his motorbike crashed into a car outside a US military base in Northamptonshire in August last year.
The Home Office submitted the extradition bid on Friday.
The 42-year-old, who is married to a US intelligence officer, is accused of driving the car that hit and killed the Northamptonshire teenager.