The 35-year-old man, who is suspected of being the target of the shooting, is being held in hospital on a prison recall after violating the terms of his licence.
He will be returned to prison to serve the rest of his sentence. He will be questioned further about the murder and is in stable condition.
Olivia Pratt-Korbel was killed on Monday night by a masked attacker who chased a man into a terraced house on Kingsheath Avenue in the city’s Dovecot district.
After hearing gunshots, her mother opened the front door, and the 35-year-old man being pursued forced his way into the house in an attempt to flee the shooter.
Cheryl Korbel, Olivia’s mother, was shot in the wrist as she attempted to close the door on the gunman, who fired indiscriminately into the house.
As she stood behind her, the youngster was fatally shot by the same bullet.
The intruder suffered gunshot wounds to his upper body and, as Olivia lay dying, was picked up and driven to the hospital by friends in a dark-coloured Audi, which has since been seized by police.
Officers arrived and discovered Olivia with a gunshot wound to the chest.
Olivia was taken to Alder Hey Children’s Hospital, where she died later that day.
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