Peaches Geldof's husband is "not in any way under suspicion of any involvement" in her death, police have said.
Kent Police said musician Thomas Cohen has not been arrested or interviewed under caution and that "there is no plan to do so".
Detective Chief Inspector Paul Fotheringham said he was clarifying the situation following recent media speculation.
Mr Cohen found Ms Geldof, 25, dead in a spare bedroom at the family home in Wrotham, Kent, on April 7.
Mr Fotheringham said at the opening of her inquest yesterday that recent heroin use by Ms Geldof "was likely to have played a role" in her death.
He has also now revealed that drugs paraphernalia was seized from the home on the day she was discovered.
Mr Fotheringham said: "Following recent speculation in the media, I would like to make it clear that Thomas Cohen is not in any way under suspicion of any involvement in Peaches Geldof-Cohen's death or our concurrent investigation into the supply of drugs.
"He has not been arrested or interviewed under caution and there is no plan to do so. The only statement he has provided related to his discovery of Peaches' body, which is a standard requirement.
A number of celebrities attended Ms Geldof's funeral"We are in regular contact with both sides of the family to keep them apprised of our progress. Our investigation into the supply of drugs is continuing and remains a live investigation.
"Inaccurate reports have also been made suggesting that no drugs paraphernalia was found at the address, with suggestions that the scene had been 'tampered' with prior to police arrival.
"While no detail will be provided around specific items, to prevent further speculation I will confirm that contrary to rumour in the media my officers did seize drugs paraphernalia from the address on 7 April. The coroner has authorised the disclosure of this information.
"Our investigation on behalf of the coroner continues and there will be no further information released at this time."
It is believed the last contact anyone had with Ms Geldof was when she spoke with a friend on the phone at 7.45pm on the night before her body was found.
Ms Geldof's mother, Paula Yates, died of an accidental heroin overdose in 2000, aged 41.
Hours before she died, Ms Geldof, the daughter of musician Sir Bob Geldof, posted a picture online showing the two of them together.
Her funeral was held at the same church as her mother's, with a host of celebrities attending the service in Davington, near Faversham.