"To deliver our Plan for Change we will reshape the state so it is fit for the future. We cannot stick to business as usual," a Cabinet Office source said.
"By cutting administrative costs we can target resources at frontline services - with more teachers in classrooms, extra hospital appointments and police back on the beat."
In the coming week, Whitehall departments will receive a letter from Cabinet Office Minister Pat McFadden with instructions to make the cuts, the Daily Telegraph reports.
It is understood that it will be the ministers and the top civil servants in each department who will be responsible for delivering those cuts.
Unions have warned that the cuts could amount to about 10% of staffing, with FDA Union head Dave Penman saying: "The idea that cuts of this scale can be delivered by cutting HR and comms teams is for the birds.
"Elected governments are free to decide the size of the civil service they want, but cuts of this scale and speed will inevitably have an impact on what the civil service will be able to deliver for ministers and the country."
Meanwhile, Prospect Union general secretary Mike Clancy similarly warned the cuts would be public-facing, and issued a warning that "a cheaper civil service is not the same as a better civil service".
He added: "Civil servants in all types of roles help the public and deliver the government's missions. Cutting them will inevitably have an impact that will be noticed by the public," he said.
The cuts have long been promised - McFadden told the BBC earlier this month that "radical" changes to the civil service were on the way, while the prime minister vowed reforms that would "unshackle" civil servants from "bureaucracy".
Disappointing growth figures and lower-than-expected tax revenues have increased the pressure on the government to find savings in the public service.
Reeves has committed against raising taxes or government budgets in her Spring Statement, due to be handed down next week - constrained by strict spending rules she set within the October Budget.
Her two main rules are not to borrow to fund day-to-day public spending and to see debt fall as a share of the UK economic output by 2029/30.
"We can't tax and spend our way to higher living standards and better public services. That's not available in the world we live in today," she told the BBC this week.
Additional pressure has come from increase government borrowing costs, which were much higher than expected last month at £10.7bn - up from £6.5bn predicted.
Global security is also a significant factor, with the government vowing to increase defence spending, which it proposed to fund via cuts to international aid.
The government has separately sought to recoup £5bn per year by 2030 via proposed changes to the welfare system, which include stricter criteria for Personal Independence Payment (Pip) and basic level of universal credit.
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