The family of Harry Dunn hope Anne Sacoolas will be brought back to the UK as Northamptonshire Police has handed its file of evidence on the teenager's death to the Crown Prosecution Service.
The US diplomat's wife refuses to return to Britain after driving on the wrong side of the road near Croughton and crashing into Harry's motorbike in August - he died later in hospital.
But there is a chance the 42-year-old could be extradited if the CPS believes there is enough grounds to charge her with a crime as her diplomatic immunity does not apply now she is in the US.
Family spokesman Radd Seiger told the Daily Mail: "Come on, let's get on with it. For us that would be a big step if an extradition request was submitted to the US.
"That would be one giant step towards achieving closure. It's not a game – this family are grieving."
Harry's parents Charlotte Charles and Tim Dunn were told about the progress by a family liaison officer on Saturday (October 19).
The file of evidence reportedly includes CCTV footage of the Mrs Sacoolas driving on the wrong side of the road near RAF Croughton, which is also used by the US Air Force as an intelligence base, eight weeks before the fatal crash.
Meanwhile calls are growing for a public inquiry over the handling of the case after Foreign Secretary Dominic Raab admitted to asking police to delay telling Harry's parents that Mrs Sacoolas had left the country.
The family believe there has been 'misconduct and a cover-up on both sides of the Atlantic', while Mr Raab said police were asked to wait 'a day or two'.
Labour's Shadow Foreign SecretaryEmily Thornberry said: “It now looks increasingly clear that the Foreign Secretary and his officials have something to hide in terms of how they responded to this dreadful tragedy, why they allowed Anne Sacoolas to leave the country, and why they delayed informing Harry Dunn's family of her departure.
"We need an urgent parliamentary inquiry to uncover who did what in this case, who took the decisions, when they were taken, and why.
"The rights, justice and answers that are due to Harry Dunn's grieving family can no longer be denied."