The 34-year-old was pulled up on the M42, east of Birmingham – a two and a half hour drive from the scene of the fatal shooting.
The driver, from Liverpool, was arrested on suspicion of assisting an offender, Merseyside Police said, and the vehicle was impounded.
Officers could not immediately confirm where on the motorway the man was arrested on Sunday night, but the M42 runs just north of Tamworth in Staffordshire, loops around Birmingham in the south-east of the city and ends where the road meets the M5 at Bromsgrove. Worcestershire.
He is the fourth man arrested over the weekend in connection with the death of Olivia, who was shot at her home in Dovecot, Liverpool, on August 22.
A 34-year-old man from Liverpool was arrested in the Runcorn area in the early hours of Sunday on suspicion of murder and attempted murder.
Two other men, a 41-year-old from Knowsley and a 29-year-old from Liverpool, are being questioned on suspicion of assisting an offender.
The warrants were executed at two properties in Liverpool on Sunday, officers said.
Last week, Detective Chief Inspector and Head of Investigations Mark Kameen said that whoever hid the weapons used in the killing “was in the same category” as the “bad guy responsible for the murder”.
Olivia’s family also urged people to ‘do the right thing’ and said: ‘If anyone knows anything now is the time to speak up. he took our baby away from us.”
The nine-year-old died after being shot at her home when a gunman chased convicted burglar Joseph Nee into the property at around 10pm.
Nee, who was rushed to hospital by friends while Olivia lay dead, suffered two gunshot wounds.
He was only recently released on license and will return to prison once he recovers from his injuries.
An autopsy determined her medical cause of death was a gunshot wound to the chest.
A policeman tried to save her life by picking her up and running to the hospital in his arms while covering the wound in an attempt to stop the bleeding.
But despite his efforts and the efforts of the major trauma team at Alder Hey Children’s Hospital, the nine-year-old could not be saved and was pronounced dead about an hour later.
Cheryl’s mother was also injured in the shooting and is still receiving treatment.
Police said two guns were used in the shooting, and both were “coolly” removed from the scene by the killer.
Detective Chief Constable and Head of Investigations Mark Kameen said: “I continue to urge anyone with information that can assist our investigation into Olivia’s tragic murder to please come forward so we can bring those responsible to justice.
“Several people have been arrested as part of this investigation.
“However, we still need the public’s help to ensure we can build a strong case of evidence to bring justice for Olivia and her family.
“I hereby appeal to anyone who may have information, however small, that could further assist our inquiries to contact us directly or anonymously and we will do the rest.”
A 36-year-old man from Huyton and a 33-year-old man from Dovecot who were arrested on suspicion of murder and two counts of attempted murder in connection with Olivia’s death have been released on bail.
