The post office expects to lose $6 billion this year. Last year the agency lost $16 billion.
"The Postal Service is quickly moving down a path that leads to becoming a massive, long-term burden to the American taxpayer," he said.
Donahoe said the rate hike may be needed because his agency's finances are so precarious and the prospects of quick congressional action are so uncertain.
The Postal Service's board of governors could decide as early as next week whether to request a special rate increase.
Under federal law the post office cannot raise its prices more than the rate of inflation unless it gets approval from the independent Postal Regulatory Commission. The Postal Service must cite exceptional circumstances in seeking an "exigent" or emergency rate hike.
Media and marketing firms that depend on postal services have said that a big rate hike could hurt their business.
They say the impact of any rate hike would be compounded if it comes along with the regular annual rate increase expected to be announced later this year.
The agency last raised postage rates on Jan. 27. At the time, the cost of a first-class stamp went up by a penny, to 46 cents.
Lawmakers are considering cost-cutting moves that include ending Saturday mail delivery and door-to-door delivery. But many lawmakers, along with postal worker unions, have resisted such changes, saying they would inconvenience customers.
Jeanette Dwyer, president of the National Rural Letter Carriers' Association, said rural customers would be especially hard hit if Saturday mail delivery ends.
"The livelihoods, and often health and well-being, of entire communities depend on the Postal Service to facilitate communication and deliver goods," Dwyer said. "In many parts of rural America there simply are no alternatives."
The Postal Service says it would like to end Saturday mail delivery. It also is seeking to reduce its $5.6 billion annual payment for future retiree health benefits. It missed two of those $5.6 billion payments last year, one deferred from the previous year, and is expected to miss another at the end of this month when its fiscal year ends.
"The pre-funding requirement has created hardships for postal workers and it threatens to destroy the Postal Service," said Cliff Guffey, president of the American Postal Workers Union.
The Senate Homeland Security and Governmental Affairs Committee is considering a bipartisan proposal to stabilize the agency's finances, including changing the method by which retiree health care costs are calculated.
Saturday mail delivery would be ended in a year and the Postal Service could start shipping alcoholic beverages to compete with private shippers such as FedEx under a bipartisan proposal by the committee's chairman, Tom Carper, D-Del., and the panel's ranking Republican, Tom Coburn of Oklahoma.