William Billingham was found dead in his cell at HMP Birmingham, where he was serving a 27-year minimum term for stabbing Mylee Billingham in a “cowardly and brutal” attack in Brownhills in January 2018.
Birmingham coroner James Bennett told a pre-inquest review it was "on the face of it" a natural cause of death from chronic obstructive pulmonary disease.
Mr Bennett added he was awaiting a report from the Prisons and Probations Ombudsman in order to determine whether Billingham could have received better care while at the Winson Green prison, which is likely to be submitted in September.
Mr Bennett told how the murderer was "found unresponsive" in his cell by a prison officer on March 19.
He said other than prescribed medication, toxicology tests had revealed "no traditional drugs misuse".
Billingham's TV star brother, Mark 'Billy' Billingham, attended the inquest remotely and said he had questions he wanted answering surrounding the killer's death.
A previous hearing was told the 57-year-old father-of-six had complained of feeling unwell and been assessed by medical staff on March 18, but that his death was not thought to be suspicious.
Addressing the coroner, Mark Billingham, best known for his role in Channel 4's SAS: Who Dares Wins alongside Ant Middleton, and a former bodyguard of Brad Pitt and Angelina Jolie, said: "Clearly everything hinges on the report in September. I do have questions and need to have answers."
He added: "I would like to air these questions before a final decision is made. It is obviously very important to us. There are not many but some definitely need answering."
A trial at Birmingham Crown Court was told that primary school pupil Mylee was stabbed in January 2018 in a “revenge” attack motivated by jealousy and anger against Billingham’s ex-partner, Tracey Taundry.
Jurors were told that Billingham, of Valley View, Brownhills, killed the youngster after dragging her into his bungalow when her mother came to collect her.
The schoolgirl's death rocked the community and prompted an outpouring of grief and sea of tributes in Brownhills.
A date for a full inquest hearing was not set but Mr Bennett said it would likely be held in November or December.