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 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 Post Office's new chairman Nigel Railton will brief staff on Wednesday on the outcome of a review launched earlier this year.
The strategic review is designed to fundamentally change how the Post Office operates.
The aim of the review is to put the Post Office 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.
Mr Ward, of the CWU, said it appeared the Post Office had "learned no lessons from its chaotic and uncoordinated mistakes from the past".
"CWU members are victims of the Horizon scandal – and for them to now fear for their jobs ahead of Christmas is yet another cruel attack," he added.
Earlier this month, Post Office minister Gareth Thomas said the organisation was at a critical juncture and the government had already commissioned its own review into what the Post Office should look like in the future.
Business Secretary Jonathan Reynolds told the inquiry on Monday that he didn't feel sub-postmasters were getting appropriate pay for the amount of business they conduct.
He hinted that Post Office branches could step into filling the gap left by High Street bank branch closures.
Ministers have been exploring plans to hand ownership of the Post Office to sub-postmasters.
Reynolds told the Horizon inquiry there was still “tremendous affection” for the Post Office among the UK public and a “desire for it to have a strong future.”
He said the Post Office “has to be one that has a significantly smaller centre" and sub-postmasters needed better pay, adding "that will necessitate some quite considerable changes to the organisation centrally to do that".
A Post Office spokesperson said that on Wednesday the organisation would be setting out a "new deal" for postmasters and for "the future of the Post Office as an organisation".
"It will dramatically increase postmasters’ share of revenues, strengthen our branch network and make it work better for local communities, independent postmasters and our partners who own and operate branches," he added.
A spokesperson for the Department for Business and Trade said: “The government is in active discussion with Nigel Railton on his plans to put postmasters at the centre of the organisation and strengthen the post office network for its long-term future.”