The 53-year-old was found with multiple gunshot wounds to the torso, according to the New York Police Department.
Shea said there has been a slight uptick in alleged mob-related violence in NY within the past year.
The account, the report reads, shows Cali exiting and shutting his front door as he approaches a driver who had struck his vehicle.
USA media reported that Cali's death marked the first murder of a NY mob boss in 34 years, since the death of Paul Castellano - another Gambino family boss - by order of the infamous John Gotti, also known as Teflon Don.
They said distraught family members ran outside after the shots were fired.
Cali is thought to have taken the helm of the Gambino family in 2015, replacing Domenico Cefalu.
The Gambino operation is said to be one of the five historic Italian-US mafia families in NY.
It was Rudy Giuliani's prosecution of the Gambinos and other mob families that led to his election as New York City mayor. The Daily Beast noted, "Cali's home is a two-minute drive from where one of his predecessors, late Gambino boss Paul Castellano, lived in an ostentatious mansion dubbed the White House until he was executed outside Sparks Steak House in Manhattan in 1985".
Gambino headed the organization until 1976, when he handed power over to his brother-in-law Paul Castellano.
The day after Castellano's December 1985 murder, The New York Times called the Mob boss' death "highly stylized", but Giuliani dismissed such morbid romanticism.
A law enforcement official confirmed to CNN that the victim was a high-ranking member of the Gambino organized crime family and is believed to be the acting boss. Castellano was the last New York City crime boss to be gunned down, and Gotti later died in prison in 2002. He was from Sicily, and sources said he brought immigrant Italian gangsters into the family, and focused on the heroin and OxyContin trade. The shooting outside Cali's home, the source said, suggests the killing was meant to send an ominous message.
"It takes a certain type of evil to murder a friend in their own home, and then console the grieving relatives", said Federal Bureau of Investigation assistant director in charge William Sweeney.
Last October, 71-year-old Sylvester Zottola, a reputed associate of the Bonanno organisation, was shot dead at a takeaway restaurant in the Bronx, New York.
The reputed Colombo boss, Carmine "The Snake" Persico died about a week ago, aged 85.