She was driving a auto that was in collision with Mr Dunn's motorcycle near RAF Croughton in 2019. Sacoolas claimed diplomatic immunity and returned to the US, but a Dunn family spokesperson suggested that United Kingdom authorities considered trying her in absence.
"The Prime Minister raised the tragic case of Harry Dunn, and the need to secure justice for Harry's family", a spokesman said.
The crash happened outside the Northamptonshire RAF base where Mrs Sacoolas's husband Jonathan worked as an intelligence officer.
The US informed the Home Office late on Thursday that it had rejected the extradition request, a decision which has been condemned by politicians and Dunn's grieving family.
Prime Minister Boris Johnson has told US President Donald Trump of "the need" for the suspect in the Harry Dunn case to return to the UK, No 10 has said.
"He reiterated the need for the individual involved to return to the United Kingdom".
Ms Leadsom held talks with USA ambassador Woody Johnson, the commander of RAF Croughton Colonel Bridget McNamara and the Chief Constable of Northamptonshire Police.
She also met with Dunn's family on Friday, the day after she had informed them of the USA secretary of state Mike Pompeo's decision to refuse the extradition request.
"I called the US ambassador earlier to express the government's disappointment about this decision", Raab said, adding that United Kingdom officials are "urgently considering our options".
She said the prime minister is "very much on the side of the family in their desire to see justice done", adding: "All of us in government are working to that end".
The State Department says Sacoolas had diplomatic immunity when she was in Britain, and to send her to face criminal charges would set "an extraordinarily troubling precedent".
The foreign secretary, Dominic Raab, has said the move "amounts to a denial of justice". "The extradition request is always going to be over Anna Sacoolas's head, and we're never going to give up", she said.