The 69-year-old became a Russian citizen in 2013 after the French government criticised his decision to move abroad because of higher taxes.
But now Depardieu has reportedly told Turkish newspaper Ayndinlik he wants to gain citizenship in Turkey.
Ayndinlik says it interviewed the actor while he visited North Korea for the secretive state’s 70th anniversary celebrations.
The newspaper features a photograph of Depardieu and an account of the actor answering its questions.
It follows a number of sightings of Depardieu in photographs of crowds in Pyongyang earlier this month.
Sporting a light straw hat and white shirt, the former actor appeared at an event celebrating North Korea’s 70th anniversary – although it was unclear if he was due to take part or was there as a guest.
Oliver Hotham, managing editor of NK News, tweeted that he had spotted Depardieu at a hotel in the city but was told by a minder that he would have a “bad time” if he persisted in asking him for a quote.
Last month, prosecutors in Paris opened a preliminary investigation into allegations Depardieu raped and sexually assaulted a 22-year-old comedian and dancer.
The actor’s representatives have denied the accusations.
Depardieu has starred in more than 200 films across six decades, including The Man in the Iron Mask, Life of Pi and Kenneth Branagh’s Hamlet.
Embraced by Russia in 2013, Depardieu met Vladimir Putin in the Black Sea resort of Sochi and called the country “a great democracy, and not a country where the prime minister calls one of its citizens shabby”.