Alexia Walenkaki was playing on a rope swing in Mile End Park when a tree trunk holding the swing fell on her.
The Met Police is compiling a report for the Crown Prosecution Service a pre-inquest review at St Pancras Coroner's Court heard.
A spokesman for the council said such a charge was "not appropriate".
About an hour after Alexia's accident, on 17 July, she went into cardiac arrest and died in the Royal London hospital.
At the time, her mother Vida Kwotuah said she watched in horror as the tree trunk - which she described as rotten - knocking her daughter to the ground.
Det Insp Craig Bradley said more expert evidence was being gathered.
He said: "We are in the process of investigating the possibility of corporate manslaughter or gross negligence. We have liaised very closely with the Crown Prosecution Service (CPS)."
The inquest heard the tree trunk was decayed and an expert has compiled a report on its state.
Mr Bradley said he has contacted another expert about the level of decay in the trunk at the time of the accident, and whether it would have been visible in an inspection.
Mark Scoggins at Fisher Scoggin Waters, solicitors representing Tower Hamlets Council, said such a charge would require "gross failings" in senior management at a "very serious level".
He added: "The issue is literally down on the ground, it is difficult to see how senior managers up the chain could have knowledge of that."
An inquest with a jury will run for four days starting on 11 April. If a criminal prosecution is brought, the inquest will be adjourned.
Tower Hamlets Council could be prosecuted for corporate manslaughter after a five-year-old girl died while playing in a park.