Saudi officials were alleged to have cut off Mr Khashoggi’s fingers and then decapitated him at the consulate as his fiancée waited outside in an account published in the Yeni Safak newspaper.
The report cited an audio recording of Mr Khashoggi’s alleged killing on 2 October.
The recording was offered as evidence a Saudi team had immediately accosted the 60-year-old journalist after he entered the consulate.
US president Donald Trump demanded Turkey hand over any audio or video recording it had of Mr Khashoggi’s alleged killing “if it exists”.
The searches and the leaks in Turkish media have ensured the world’s attention remains focused on what happened to Mr Khashoggi – a Washington Post columnist who went into a self-imposed exile in the US over the rise of Saudi Crown Prince Mohammed bin Salman.
Labour leader Jeremy Corbyn has called for the suspension of arms sales to Saudi Arabia – a key US ally – following the journalist’s alleged murder.
The search of the consul’s residence came 15 days after Mr Khashoggi’s disappearance – and after police apparently thought they would be able to conduct the search on Tuesday. Turkish foreign minister Mevlut Cavusoglu said Saudi officials had halted the earlier search, claiming Consul General Mohammed al-Otaibi’s family was still there.
Al-Otaibi had been reported as being heard on tape telling those allegedly torturing Mr Khashoggi: “Do this outside; you’re going to get me in trouble.”