"Pirates have contacted us to put forward their demands, we are in talks with them," Spyros Minas, Alloceans Shipping general manager, said.
He declined to disclose how much they were demanding for the ship's release.
The Ariana cargo ship was seized by pirates 250 miles southwest of the Seychelles in the Indian Ocean. The ship was en route to the Middle East from Brazil and was carrying 35,000 metric tons of soya. The pirates escorted the ship to the Somali port of Hobyo.
The Ariana's Ukrainian crew are reported to be in good health and have sufficient food and medicine.
Since the start of this year, almost a hundred vessels have been attacked by Somali pirates. A number of countries, including Russia, have deployed warships to protect the Gulf of Aden.
As of May 5, Somali pirates were reported to be holding 17 ships and some 300 crew.