Saudi Arabia had vehemently denied that Khashoggi was detained after he entered the consulate.
An official, speaking to Reuters news agency, said Jamal Khashoggi was killed in a premeditated murder and his body removed from the consulate.
The Turkish sources did not say how they believed the killing was carried out.
"The idea of kidnapping of a Saudi citizen by a diplomatic mission is something that should not be [propagated] in the media" he said.
Saudi Arabia's consul-general rejected claims about a possible abduction, telling Reuters that his country was helping search for Khashoggi.
The journalist has lived in self-imposed exile in Washington for the past year, fearing retribution for his views on Saudi policies. He has not been heard of since.
The United States is seeking more information, a State Department official said.
Another official confirmed the story.
He was seeking to secure documentation for his forthcoming marriage when he entered the Saudi consulate in Istanbul.
The Turkish source said Turkish officials were trying to identify them.
The Saudis have since all left Turkey.
The disappearance of Khashoggi could threaten the already fragile relationship between Saudi Arabia and Turkey.
Relations between the two countries are already strained after Turkey sent troops to the Gulf state of Qatar past year in a show of support after its Gulf neighbors, including Saudi Arabia, imposed an embargo on Doha.
The Lebanese al-Akhbar newspaper said that the journalist had been flown to Saudi Arabia with the apparent consent of the Turkish intelligence authorities. But he also criticized Turkey's crackdown following a 2016 failed coup against Erdogan.
The crown prince insisted that the kingdom has always paid for armaments from the US.
The idea that Khashoggi may have been abducted at the consulate was "disgusting", he said.
The Turkish official news agency reported Saturday that the public prosecutor's office has started an investigation into his disappearance and the rumors that Khashoggi was detained had "deepened". His fiancee, who had waited outside, said he never came out. It's there since 1744; I believe more than 30 years before the United States of America, And I believe, and I' m sorry if anyone misunderstands that, but I believe President (Barack) Obama, in his eight years, he worked against many of our agenda not (only) in Saudi Arabia, but also in the Middle East.
"I have left my home, my family and my job, and I am raising my voice", Khashoggi wrote in September 2017. "Ever since the relationship started between Saudi Arabia and the United States of America, we've bought everything with money", he said, adding that since Trump came to power, the the kingdom chose to purchase over 60 percent of its needed armament from the U.S. for the next 10 years. "Jamal was - or, as we hope, is - a committed, courageous journalist". Yesterday, Turkish authorities said he had been murdered.