The Greek navy is racing to intercept the vessel, called Blue Sky M and flagged to Moldova, which is carrying passengers from Turkey to Croatia.
The ship sent a distress signal because of armed people aboard, Greek state television has reported.
But amid mixed reports, some have suggested the ship may simply have had engine trouble.
A flyover of the ship by Greek authorities showed no movement on the deck of the ship, according to Greek media.
It is currently to the north west of Corfu, Greece, travelling on an itinerary to Croatia.
However, the ship seems to have made an unscheduled change of direction, Channel 4 News understands, from the path taken by the ship as shown on MarineTraffic.com.
It is now heading in the direction of the southern coast of Italy.
Reports indicate that asylum seekers from Syria may be on board.
Roy Paul, programme director at the Maritime Piracy Humanitarian Response Centre, told Channel 4 News that this was unlike any case he has heard of and could be a hijacking.
“This is totally different scenario. Usually we deal with cases off the coast of Somalia to hold for ransom. This is in European waters. It’s totally different. Our concern would be for the crew of the vessel.”
“If they want to take it to the Italian coast, one would assume the Italian navy would try to intercept them. Perhaps on board the ship there were illegal immigrants who may have taken control of the vessel.”
He said it was unlikely to be a case of ransoming the ship.
“Where is the financial gain? No-one’s going to pay ransom for illegal immigrants.”