In early January Hearst announced it might cease printing the 145-year old newspaper, which has a circulation of more than 127,500, if it cannot find a buyer in 60 days and continue it online.
The Wall Street Journal is reporting today that journalists at the Seattle Post-Intelligencer have been approached in recent days about working for an online-only publication.
If the paper went digital-only it would follow in the footsteps of the US daily newspaper the Christian Science Monitor, which in October said it was to scrap its daily print issue after 100 years and focus on running its website.
A print-only future for the Seattle Post-Intelligencer, which lost $14m last year, would likely mean many staff on the paper on the editorial and commercial side of the business would lose their jobs as the revenue from print ads ended.
The Seattle Post-Intelligencer could be the first of many US newspapers to either cease publication entirely or go online only.
Hearst has not said when it might stop publishing the print edition, but the WSJ reported that journalists on the publication who are working on stories about the paper's history for a final edition have been told to file their stories by the end of the week -- indicating the final day for a print publication might come early next week.
The paper also said that those being asked to work on a possible online-only version of the Seattle Post-Intelligencer are young with experience of blogging and covering breaking news online.
Rival The Seattle Times, co-owned by Miami Herald publisher McClatchy, 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.
Another Hearst title that could face a similar future is its flagship San Francisco Chronicle, which last month the media giant said faced closure.
The San Francisco Chronicle is losing $50m a year and is the West coast city's main newspaper.
The possible closure of the Seattle Post-Intelligencer follows EW Scripps ceasing publication of the Rocky Mountain News last week as the US newspaper market continues to deteriorate .
Earlier this week USA Today publisher Gannett had its debt rating cut to junk status as Philadelphia Newspapers, which filed for Chapter 11 bankruptcy protection last week, announced it would publish its tabloid Philadelphia Daily News as an edition of sister paper the Philadelphia Inquirer in an effort to cut costs.
Blog coverage of the US newspaper crises on Gordon's Republic