Janma Joshi and her son Jai, were killed in the blaze which swept through their two-bedroom property in the Tuebrook area of the city last week.
An inquest into the deaths opened yesterday and heard that police were "satisfied" the 40-year-old woman had started the fire using accelerants.
"Investigations are still ongoing into the circumstances of the fire, but I am satisfied the fire was started deliberately with the use of accelerants within the premises," Detective Chief Inspector Andy O'Connor of Merseyside Police told Liverpool Coroner Andre Rebello during the hearing.
The inquest heard that Janma Joshi was born in Malawi and worked as a pharmacy assistant in England.
She was married to Mohit Nanda, who is believed to be serving as an officer in the Indian merchant navy.
He was not Jai's father, who is a member of a Lancashire-based Patel family, which released a statement in memory of the boy.
"Jai was a model child who tragically lost his life to a mindless act. The life of our beloved Jai has been lost at such a tender age. A tragedy, yes, with many open questions, said the statement," the statement said.
Jai was a pupil at Howick CE Primary School in Penwortham, near Preston, where his father is believed to live.
Headteacher Deborah Bramley said,"We are all in shock at the news of Jai's death and extremely upset. He was a completely endearing little boy with a big smile and the older children all tended to look after him because he was quite small. He was very happy in school. We will miss him enormously".
Local police have called for anyone with more information to come forward as inquiries are still ongoing in the case.