Hearst said that it might shut down the 145-year old newspaper if it cannot find a buyer in 60 days. If shut it could continue as a digital-only newspaper.
If it is closed the paper, which has a circulation of more than 127,500, would be the biggest victim of the downturn that is hitting the US newspaper. It would also put the spotlight on some of Hearst's other newspaper titles, which include the San Francisco Chronicle and the Houston Chronicle.
If the paper went digital only it would be following in the footsteps of the Christian Science Monitor, which in October announced it was to scrap the daily print issue after 100 years and focus on running its website.
The Post-Intelligencer has been losing money for a number of years. In 2008 it lost $14m and is expected to lose more in 2009.
Steven Swartz, Hearst Newspapers President, said: "Our losses have reached an unacceptable level, so with great regret we are seeking a new owner for the P-I."
In a separate memo to employees, reported by Reuters, Hearst Corp Chief Executive Frank Bennack, Jr said: "Nothing we are doing here today is meant in any way to suggest that we don't believe in the future of print publishing in our other newspaper markets."
Rival The Seattle Times has a circulation of more than 215,000 copies and the two papers have a joint advertising, production, marketing and circulation operation under a joint operating agreement.
The Seattle Times is co-owned by Miami Herald publisher McClatchy and the Blethen family, who run the joint backroom operations.
The news of the possible demise of the paper came on Friday as The Globe and Mail in Canada said it was planning to cut its work force by 10%, resulting in the loss of 80 to 90 jobs.
The paper is owned by CTVglobemedia, a private company that also owns Canadian TV network CTV.