The agency also wants to set up its own benefit systems for retired employees.
Congressional approval would be needed for either step, and both are expected to face severe opposition from postal unions, which have contracts that ban layoffs.
The post office has cut 110,000 jobs over the last four years and is currently engaged in eliminating 7,500 administrative staff. In its 2010 annual report, the agency said it had 583,908 career employees.
Postal officials have said they will be unable to make a $5.5 billion payment to cover future employee health care costs due Sept. 30. It is the only federal agency required to make such a payment but, because of the complex way government finances are counted, eliminating it would make the federal budget deficit appear $5.5 billion larger.
Postal officials have sought congressional assistance repeatedly over the last few years, including requests to be allowed to end Saturday mail delivery, and several bills have been proposed, but none has been acted on.
The post office recently said it is also considering closing 3,653 post offices, stations and other facilities in an effort to save money. Offices under consideration for closing are largely rural with little traffic.
The Associated Press contributed to this report.