Though the audio recording does not conclusively implicate Crown Prince, analysts say it's an important clue.
The 59-year-old Saudi dissident was last seen entering the consulate on October 2 to obtain documents for his upcoming marriage.
Turkish President Recep Tayyip Erdogan has said the 15-member Saudi team travelled from Riyadh to Istanbul to kill Khashoggi.
Erdogan did not elaborate on how and when the Saudi official heard the recording of the killing of the Saudi citizen.
"At the current stage we believe an worldwide investigation is a must", Foreign Minister Mevlut Cavusoglu was quoted as saying by the state-run Anadolu news agency.
He has gone back and forth between demanding full accountability for the journalist's murder and emphasising the strategic importance of the US-Saudi alliance, going so far as to say any punishment imposed on Riyadh will not include a halt to US arm sales.
The Turkish Government allowed US CIA Director Gina Haspel to listen to the audio recording of events that took place inside the consulate and to the telephone conversations that took place between the team and Saudi Arabia, a senior Turkish official said.
The bet by Kushner, a real estate developer, on Saudi Arabia's brash young crown prince, has come under intense scrutiny following the murder of Washington Post columnist Jamal Khashoggi at the Saudi consulate in Istanbul on October 2.
Erdogan told reporters that after the intelligence officer had heard the recording, he said: "I guess they were on heroin; only someone who is on heroin would do such a thing".
A member of parliament from the opposition Republican People's Party (CHP), Engin Altay, said that the Turkish government did not share the Khashoggi murder recordings with parliament.
Democratic Sen. Chris Van Hollen said he expects to see significant sanctions against the Saudis "targeted to the highest levels of the Saudi government". But four sources based in the Gulf told Reuters this week that he was still at liberty and continued to operate discreetly.
The assertion is backed up by Turkish intelligence officials, who told their American counterparts that Mutreb was speaking to one of Prince Mohammed's aides, the Times reports.
He also supervised the brief detention, humiliation and beating of Lebanese Prime Minister Saad al-Hariri past year. The images are said to have been taken as the Saudis passed through security checks at the terminal when they left the country.
The quote was confirmed by three sources familiar with the recordings. These had led Ankara to conclude from an early stage that the killing was premeditated, despite Saudi Arabia's initial denials of any knowledge or involvement.
American intelligence officials believe is a reference to Saudi Arabia's Crown Prince.