Kent police have said that there is an "ongoing investigation into the supply of drugs" that played a part in the journalist and TV presenter's death, although they confirmed that "there have been no arrests at this stage."
Peaches' husband Thomas Cohen could be questioned as part of the investigation.
Peaches Geldof and Thomas Cohen
On Thursday the inquest into the 25-year-old's untimely death on 7 April heard that Thomas found his wife's body in the spare bedroom of the Kent home they shared with their two sons, Astala and Phaedra.
He arrived at the Wrotham property with his mother Sue on the understanding that his wife may have been sleeping. On discovering her body, he located their 11-month-old son Phaedra before trying to resuscitate her and calling to his mother to ring the emergency services.
Peaches Geldof with husband Thomas Cohen and son Astala
Police found no evidence of drug paraphernalia in the house, leading to speculation that it may have been removed before their arrival.
Peaches herself had a long history of drug use, including reports she had to be revived after an overdose in 2008. Friends said she had stopped using drugs before the birth of her children.
According to the Times, there was speculation that she might have accidentally overdosed because her body could not tolerate the quantities of heroin she had previously taken.
The inquest has been adjourned until 23 July.