Two people close to Khashoggi, one of whom is his Turkish fiance, raised concerns about his whereabouts, saying he failed to emerge from the consulate.
The woman, who asked not to be named, said on Tuesday she had waited outside the consulate from 1pm local time (11am BST) and called the police when he had not reappeared.
"I don't know what's happening. I don't know if he's inside or if they took him somewhere else," she said by telephone from outside the compound.
Concerns were raised further after Saudi Arabia's official SPA news agency reported on Tuesday that an unnamed Saudi national was arrested and extradited to the kingdom by its Interpol agency.
Turkish and Saudi authorities, including the Istanbul consulate and the Saudi embassy in Washington, did not immediately respond to requests for comment.
Khashoggi fled Saudi Arabia in September last year after authorities banned him from writing in response to his criticism of the kingdom's rulers and US President Donald Trump.
Since then he has been in self-imposed exile in the United States, writing for The Washington Post.
In statement on Tuesday, the Turkish Arab Media Association said it was "concerned" for Khashoggi, and urged Riyadh to comment on his disappearance.
At least 11 journalists are currently detained in Saudi Arabia, according to the CPJ and RSF.
Saudi Arabia, which ranks 169th out of 180 on an RSF World Press Freedom Index, has promoted a modernisation campaign since the 2017 appointment of Prince Mohammed bin Salman as heir to the throne.
But the ultraconservative kingdom, which won plaudits in June for lifting a ban on women driving, has drawn heavy criticism for its treatment of dissent and human rights campaigners.
Prince Mohammed has presided over one of the worst crackdowns on journalists, clerics and activists, some of whom face the death penalty for trumped up charges of terrorism.
