Fairfax Media reports the service's 32-thousand staff will be told of the job cuts on Tuesday.
It says most of the jobs will go in Melbourne and Sydney, as Australia Post faces losses running into the billions if it continues to offer its failing letters delivery business.
Finance Minister Mathias Cormann has ruled out selling off Australia Post for now.
"Australia Post is obviously facing some structural challenges, job losses are always disappointing but the truth is that Australians write fewer letters," he told Sky News on Sunday.
While the government had considered the Commission of Audit recommendation to privatise Australia Post, it didn't think the time was right.
"I'm not going to rule out what may or may not happen in the future, but right now we've made a decision that it's not sensible to proceed with a possible sale of Australian Post," Senator Cormann said.
Acting Prime Minister Warren Truss said Australia Post faced a crisis in relation to falling revenue from standard letter deliveries. "They are doing well, obviously in parcel delivery ... but that represents a substantial change in the nature of the business," Mr Truss told ABC TV.
He said maintaining mail services in remote and regional communities should be a priority.
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