Peaches Geldof's husband is not suspected of playing a hand in her death, according to police.
According to Kent police, musician Thomas Cohen has so far not been arrested or interviewed under caution and neither are such plans underway, the Guardian reported.
Det Ch Insp Paul Fotheringham said that he was making his position clear following recent speculation in the media.
Cohen had found Geldof dead in a spare bedroom at their family home in Wrotham, Kent, on April 7.
Fotheringham had previously said that recent heroin use by 25-year-old Geldof "was likely to have played a role" in her death.
