Two first mates, one second mate and a chief engineer have been detained on allegations they failed to protect passengers, according to the Associated Press news agency.
The four crew members are also reportedly accused of abandoning the ship.
AP says prosecutors are considering whether to apply for a formal arrest warrant to allow for a longer period of investigation.
The ferry's captain and two other crew members have already been arrested on suspicion of negligence and abandoning people in need.
More top news
The Salisbury nerve agent attack has heightened tensions between Russia and the West. What is it like to be caught in the middle of the two?
The former national team boss was accused of intimidating a female official with a pole following the Lionesses' semi-final Euros defeat.
Cloudy at first in the south, with patchy rain slowly clearing and turning brighter.