The ransom demand is expected from the hijackers of a Japanese tanker near Somalia's coast.
The U.S. Navy is tracking the Golden Nori as the pirates hold hostage its 23 crew members - nine Filipinos, two South Koreans and 12 Myanmar citizens.
On Sunday, a U.S. destroyer fired at and destroyed two pirate boats tied to the ship, which is loaded with highly flammable benzene.
Josefina Villanueva - the sister of crew's Filipino supervisor, 48-year-old Laureano Villanueva - told The Associated Press in Manila that the pirates let the ship's Filipino captain call his wife and relay the message that all on board were "OK," and that "nobody aboard the boat was harmed."
She said that she got the information from the Philippine Department of Foreign Affairs, and that the department also told her the ship was anchored in Somalian waters.
"The pirates are still on board with the crewmen. They cannot leave," Josefina Villanueva said.
Asked if a ransom was being demanded, she said: "The talks are just starting. I think the pirates will later on demand something."
Separately, Philippine Foreign Affairs Undersecretary Esteban Conejos said the government is "doing everything" to save the crew, but cannot disclose details.
Conejos said there has been no direct contact between the Philippine government and the pirates.
"We won't talk directly to them. We talk with the host government or the Filipinos' employer, in this case the Japanese company" that owns the ship, he said. "We're hoping for the best. We're praying for the best."
"The problem is there is no central government in control (in Somalia)," he said.
Villanueva said the Filipino sailors' families were being updated regularly by the Department of Foreign Affairs and officials of Seacrest Maritime, an agency that recruited the Filipinos to work on the ship.
She said her brother, the eldest of nine children, is the "family breadwinner, a very loving person, very kind."
"We're very worried. All of us are worried. We want to ensure the safety of our brother," she said. "We're holding daily prayers in our house. his family and other relatives all come. I hope the government can help us deal with this problem so my brother could be free again."
Having little information, the family has been checking the Internet daily for any news, she said.
In 2011, Russia signed a 1.2 billion-euro contract with France for the construction of two Mistral-type vessels