Nee was jailed in 2009 for serving as a 'trusted foot soldier' in a drugs gang that help push heroin and crack cocaine onto the streets of Liverpool
Career criminal Joseph Nee, who has been arrested and will be questioned about the murder of the little girl, was also shot in the incident on Monday evening
Olivia was fatally injured and Ms Korbel was shot in the wrist as she tried to shut the door
The gunman then fired two more times through the gap in the door, hitting Nee in the upper body, before running away
The 35-year-old was then driven away in a black Audi, while Olivia and Ms Korbel were left behind.
The gunman was described as about 5ft 7in (170cm), of slim build, carrying a handgun and wearing a black padded jacket, a black balaclava and black gloves
Nee had been jailed for three years and nine months in 2018 for burglary and was previously convicted of two counts of theft of a motor vehicle, dangerous driving, driving without insurance and driving while disqualified.
Previously Nee was jailed for six-and-a-half years in 2009 for serving as a 'trusted foot soldier' in a drugs gang that help push heroin and crack cocaine onto the streets of Liverpool.
While not identifying him by name, police have said a man injured in the shooting would be recalled to prison for allegedly breaching the terms of his licence conditions with "poor behaviour".
Police said the man, who was in a stable condition, had been detained in hospital and would be "further questioned" in connection with Olivia's death.
The force also said officers had been given the same name by two different sources in the hunt for the gunman.
Both men have no links to Olivia's family, police have said.
Nee, the intended target of the shooting that left little Olivia dead in her home in Liverpool has been described as a “trusted foot soldier” who had bragged that life behind bars was like a holiday in Butlins.
Photographs of Nee reportedly taken in HMP Kirkham in 2019 and shared on social media by an accomplice, show him standing in the sun with a group of men as he bragged about life behind bars in captions which reportedly read 'Butlins with bars' and 'costa del Kirkham'.
Kirkham is an open prison which houses 650 men in 24 units. Each unit has a phone and a kitchen, and prisoners have access to a gym and snooker and pool tables.
Det Ch Supt Mark Kameen said the force was "absolutely dedicated" to ensuring there were sufficient resources to investigate Olivia's death, as well as the recent shootings of 28-year-old Ashley Dale in Old Swan and 22-year-old Sam Rimmer in Dingle.
He said each case was "receiving first-class treatment and will continue to do so" and that police raids carried out across Liverpool earlier were in response to the deaths and organised crime.
"In effect, Merseyside Police [is] baring its teeth," he said.
"We're proactive, we're hard-edged and we'll take the fight to the criminal," he added.
Referencing Merseyside Police's recent watchdog grading of outstanding for its efforts in tackling organised crime, he said the force was "not asleep here in any way".
"This hasn't suddenly jerked us into some sort of activity," he said.
"This is daily business for Merseyside Police but now we're just ramping it up even further."
In a tweet, Prime Minister Boris Johnson said the shooting was "horrific" and "senseless" and that his thoughts were with Olivia's family and "the people of Liverpool".
He added that Merseyside Police would get "whatever they need to catch those responsible and secure justice for Olivia".
Liverpool Mayor Joanne Anderson tweeted that "someone out there knows who did this", adding: "For Olivia, and for the safety of our city's communities, you must come forward."
Mr Kameen said inquiries were continuing "into the shocking murder of Olivia" and the force was "supporting her family as they try to come to terms with this tragedy".
"I would like to echo the words of our chief constable yesterday [and] appeal to the community to keep helping this family in every way possible," he said.
He added that this was "not the time for anyone who knows who was responsible to stay silent".
"It is a time for us all to make Merseyside a place where the use of guns on our streets is totally unacceptable and those who use them are held to account.
"If you saw, heard, captured or know anything, tell us directly or anonymously and we will continue to act."
Speaking while on a walk around the area with Merseyside Police and Crime Commissioner Emily Spurrell and Liverpool City Region Mayor Steve Rotheram, Chief Constable Serena Kennedy said people were "angry this is happening in their communities, where some have lived for many years".
"They feel frightened about what's happening, but the feedback I have received is that they feel grateful for the additional support and resources we are providing, including a high visibility police presence," she said.
Ms Spurrell said she was "really pleased" to hear information about who was responsible for Olivia's murder had been shared with police.
Encouraging others to get in touch with any information they may have, she said "we know somebody out there will know what happened and who is involved".
Paying tribute on Monday, Olivia's head teacher Rebecca Wilkinson said St Margaret Mary's Catholic Junior School in Huyton was in "shock and disbelief".
She said Olivia was "a little ray of sunshine" and was a "lively little soul [who was] very, very popular with all her peers".
Tributes to Olivia have been left by friends and neighbours of her family.
Jean Martindale, whose grandson was in the same class as Olivia, said he had "taken it really badly".
"Yesterday was terrible for all the children, but he was close to Olivia... and he was very, very sad," she said.
Ms Martindale, who has lived in the area for 52 years, said Olivia's death had been "absolutely devastating" for their close-knit community.
"You can feel it, the atmosphere in the air, it's horrible," she said.