The president said he was waiting for a full report on what happened to the US writer from his secretary of state Mike Pompeo.
Turkish authorities had said they believe Mr Khashoggi, a Washington Post columnist, was murdered at the Saudi consulate in Istanbul on October 2.
Saudi Arabia has denied the allegations.
Asked about the audio clip on Wednesday, Mr Trump said: “We have asked for it, if it exists. I'm not sure yet that it exists, probably does - possibly does.”
Turkey's pro-government Yeni Safak newspaper published what it said were details from audio of his torture and interrogation.
Mr Khashoggi was killed within minutes and his torturers severed his fingers during the interrogation, the newspaper said.
His killers later beheaded and dismembered him, it added.
Turkish sources said the authorities have an audio recording indicating Mr Khashoggi was killed inside the consulate.
He has not been seen since entering the building.
The US and allies have collected some intelligence which partly confirms the existence of the audio, according to reports.
But Turkey has not shared the evidence directly, sources told Reuters news agency.