More than 100 Post Office branches and hundreds of head office jobs are at risk as part of a radical shake-up of the business, the BBC understands.
Under the plan, 115 loss-making branches wholly owned by the Post Office could be closed.
The Post Office is looking at options including alternative franchise arrangements where another operator or third party could take on the branches, which currently employ about 1,000 workers.
The Communication Workers Union (CWU) said that for the company to propose such plans as the public inquiry into the Horizon IT scandal continues was "immoral" and "tone deaf".
"We call on the Post Office to immediately halt these planned closures," said Dave Ward, general secretary of the union.
The strategic review, led by the Post Office’s new chairman Nigel Railton, is designed to fundamentally change how the Post Office operates.
It aims to put the business on a firmer financial footing, but it comes as the troubled organisation remains the subject of a long-running inquiry into the Horizon scandal.
Between 1999 and 2015, hundreds of sub-postmasters were wrongly prosecuted after faulty computer software made it appear money was missing from their accounts.
The inquiry is in its final week of evidence, more than two and a half years since it started hearings in public.
Mr Railton previously told the inquiry that a new deal was needed for sub-postmasters, to put them at the centre of the business.
The former boss of Camelot was appointed interim chairman of the Post Office after his predecessor Henry Staunton was sacked in January.
The Post Office, which is owned by the government, has 11,500 branches across the UK, most of which are franchises. Of this number, 115 are Crown Post Offices in city centres staffed by Post Office employees.
The organisation faces a host of other challenges, such as fewer people sending letters, the rise of online shopping, with revenues for its branches being hit as a result.
Mr Railton said that the plans set out would provide more than £250m each year to postmasters by 2030, although added this would be subject to government funding.
It also aims to improve branches’ banking offer for customers, and will see a "lower-risk, better value" IT system introduced for sub-postmasters.
On Monday, the European boss of Fujitsu, the company which developed the faulty Horizon system, admitted he "does not know" if the software is currently reliable.
A survey in September revealed almost seven in 10 sub-postmasters have experienced an "unexplained discrepancy" on the Horizon system since January 2020.