Alexia Walenkaki was playing on a zip line in Mile End Park, Tower Hamlets on 17 July 2015 when the tree trunk it was attached to fell on top of her. The five-year-old went into cardiac arrest and died an hour later.
Initially the Met Police and Health and Safety England were jointly investigating her death. However the Met Police is now investigating a possible charge of corporate manslaughter or gross negligence, and is compiling a report for the Crown Prosecution Service.
A spokesman for the council said such a charge was "not appropriate" at a pre-inquest review held at St Pancras Crown Court.
The tree trunk holding the swing was partially decaying, and investigations are looking at whether that decay should have been picked up by an inspection.
Tower Hamlets Council's solicitor Mark Scoggins suggested such a charge would require senior management to have direct knowledge about the tree trunk's state, which he believed was unlikely.
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.