The death of Olivia Pratt-Korbel is believed to have been caused by a dispute between family-based crime groups.
The nine-year-old was shot dead during a bungled assassination on August 22 when a gunman fired into her family home at around 10pm.
Olivia was at home with her mum Cheryl Korbel and older siblings when the gunman attempted to force entry and fired shots into the Dovecot address.
The killer had been targetting Joseph Nee, who forced his way into the house when Ms Korbel opened the door to see what was going on outside.
Despite Ms Korbel's attempts to keep the gunman out, he managed to fire a shot which hit the 46-year-old in the wrist and then struck Olivia.
He then wounded Nee in the torso and legs.
The killing happened on the 15th anniversary of the shooting of 11-year-old Rhys Jones, who died in the same city after being gunned down by teenager Sean Mercer in a failed attempt to target gang rival Wayne Brady.
The Liverpool Echo reports that tragedy had its background in clashes between the Croxteth based 'Crocky Crew', of which the 16-year-old Mercer was a member, and the Norris Green based 'Strand Gang', also known as the 'Nogga Dogz'.
However, the Echo understands that the circumstances leading up to Olivia's death are not rooted in area-based street gangs with generally younger members.
According to sources in the community, the lethal violence that crossed the threshold from the street into Olivia's home is believed to relate to a falling out between two notorious family-based gangs with roots in the east of the city.
The Echo understands the dispute may involve one side's attempts to "fill a power vacuum" created when a senior criminal was sent to prison, and is not related to gang members straying into "rival turf", as Brady did before Rhys Jones was killed.
Merseyside Police have so far arrested two men, aged 36 and 33, on suspicion of Olivia's murder, while Nee aged 35, suggesting the investigation is not focused on teenagers.
The Echo reports that the two family-based gangs involved have a long history of involvement in drugs trafficking, as well as firearms offences.
Merseyside Police could not comment on the claims. Last week, during a Merseyside Police press conference, Detective Chief Superintendent Mark Kameen was asked whether specific, defined organised-crime groups had been identified as involved in the dispute leading to Olivia's murder.
He said: "We are absolutely reviewing all of the intelligence around each of our organised crime groups that we believe operate in that area.
“We are looking at feuds ongoing at this time and historically as well.
"Every avenue of investigative opportunity is being exploited. I can't go into the details of where those OCGs sit, who was involved, for obvious reasons."
The two men arrested on suspicion of Olivia's murder have been released on bail, but the 36-year-old has also been recalled to prison on licence.
Anyone with information is asked to message @MerPolCC on Twitter or contact @CrimestoppersUK on 0800 555 111.
If you have any CCTV/dashcam/smart doorbell footage that could help inquiries, they can be downloaded on the dedicated public portal for Olivia's murder, which will go straight through to the investigation team. Footage can be submitted here.
