The US president said he had tried to get Anne Sacoolas and the 19-year-old's parents to meet so they could "grieve together" when he met them earlier this month.
The following day Charlotte Charles and Tim Dunn's lawyer Radd Seiger, said Mr Trump had "ambushed" them when he revealed Ms Sacoolas was in a nearby room.
Northamptonshire Police have interviewed Ms Sacoolas in the US in connection with the 19-year-old's death. She is believed to have been driving on the wrong side of the road when she hit the teenager's motorbike outside RAF Croughton in August.
The 42-year-old claimed diplomatic immunity after the incident and returned to the US sparking an international controversy.
"Very nice people," the president told Brexit Party leader Nigel Farage on his LBC Radio show, adding that he had set up a meeting between them and Ms Sacoolas "but all of a sudden I guess lawyers got involved."
He said she "brought a very compelling story to tell."
He added: "They were in separate rooms and what I wanted was to introduce them to each other so they could really grieve together - the parents didn't want to meet her."
Asked if there were circumstances where Ms Sacoolas could come back to the UK to face charges, Mr Trump said: "Well, I would have to see what the final facts are and, I'll take a look at the final facts. She's represented by a lawyer.
"As you know, the parents are represented by a lawyer and from the time I talked to Boris to the time I met with them, but they were both right next to each other in the White House. I was in the Oval Office with the parents and the young lady was in a room right next to the Oval Office, but the parents decided, in their wisdom, and it is certainly their choice, not to see her.
"I can understand that too."
Family spokesman, Mr Seiger said they were aware of the radio interview and the possibility of Ms Sacoolas returning to the UK being discussed.
He tweeted: "That has been the family's position all along and remain[s] so today. She must come back and we urge her to do so for her sake as well as the family's."
Northamptonshire Police said they have passed the details of their interview to the Crown Prosecution Service for consideration.
1/ We are aware of today's interview between @Nigel_Farage and @realDonaldTrump on LBC where the possibility of #AnneSacoolas's return to the UK to face justice was discussed. That has been the family's position all along and remain so today. She must come back and we urge..— Radd Seiger (@RaddSeiger)October 31, 2019
Chief Constable Nick Adderley had faced calls from Dunn's family for his resignation after he commented on potential legal action by them against Ms Sacoolas by saying: "How sad but how predictable."
Mr Adderley has deleted the tweet and apologised.
The Dunn's lawyers have since instructed the family that they should now take legal action against Northamptonshire Police for their conduct throughout the investigation.