Yasin Aktay said the "only logical conclusion" was that those who killed the journalist in Istanbul destroyed the body "to leave no trace behind".
A Saudi national and well-known critic of Saudi rulers, Khashoggi was killed and his body dismembered on 2 October.
No forensic evidence has been provided to support the claim the body has been dissolved.
"The reason they dismembered Khashoggi's body was to dissolve his remains more easily", Mr Aktay - advisor to Turkey's president - said in an interview with the Hurriyet Daily newspaper.
"Now we see that they did not only dismember his body but also vaporized it."
The claims come as Khashoggi's fiancée, Hatice Cengiz, called on world leaders to "bring the perpetrators to justice", in an editorial for five newspapers, including the Guardian and the Washington Post.
Meanwhile, reports quote Saudi Crown Prince Mohammed bin Salman as telling the US he considered murdered journalist Jamal Khashoggi to be a dangerous Islamist.
The reported phone call to the White House came before Saudi Arabia admitted Khashoggi had been killed inside the Saudi consulate in Istanbul.
Saudi Arabia has denied the comments were made or that its royal family was involved in the killing, and says it is "determined to find out all the facts".
Istanbul's prosecutor confirmed on Wednesday that the writer was strangled.
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