A second pirate identifying himself as Bile Hussein, and a Somali official in Puntland who asked not to be named, both said the Quest is between Yemen and Somalia, heading for Puntland, on Somalia's northern tip -- a haven for pirates.
"All relevant U.S. agencies are monitoring the situation, working to develop further information, assess options and possible responses," said Matt Goshko, a spokesman at the U.S. Embassy in Nairobi, Kenya, according to The Associated Press.
The 58-foot S/V Quest is owned by Jean and Scott Adam, who have been sailing the boat around the world for the past seven years. As they approached the notoriously hostile waters off the Horn of Africa, the Adams cut back using their radios and satellite systems so their location couldn't be tracked by pirates, but they were still found.
The Adams are members of the Del Rey Yacht Club in Marina Del Rey, Calif. Contacted by ABC News, a marina manager there said he knew of the situation, but was unwilling to comment or give further details at this time.
The couple details their travels on a website, where an entry from last December listed their expected stops in 2011 as "Galle, Sri Lanka; Cochin, India; Salalah, Oman; Djibouti, Djibouti; The Suez Canal; and Crete. That gets us to April."
That path would have taken them directly into the pirate-infested waters off the coast of Somalia. Pirates there have seized oceangoing vessels for large ransoms; just last week two supertankers carrying oil were seized in waters far off the Somali coast.
If the yacht reaches Somalia, the four hostages would likely be taken inland, which would make a fast resolution much less likely.
Burnet added that though the Adams have several strikes against them, including their Western yacht and their Christian ministry, which is despised by Somali jihadists, the couple are far more valuable to them dead than alive.
Pirate seizures have continued in the waters off East Africa despite the constant patrols of by the world's navies, including ships from the United States.
On Thursday, Abdiwali Abdiqadir Muse was sentenced in New York to 33 years in prison for kidnapping and brutalizing Capt. Richard Phillips, who was held hostage for five days in 2009 when pirates armed with AK-47s scrambled up the stern of Maersk Alabama.
The U.S. Fifth Fleet, based in Bahrain, coordinates an international task force that patrols the waters of East Africa. The European Community also maintains a separate anti-piracy mission in the same waters.
ABC News' Dana Hughes, Steven Portnoy, Kevin Dolak, Luis Martinez and Jeremy Hubbard contributed to this report.