The Treasury has written to government departments warning most ministers they will have to cut up to 10% of their budgets for the year 2015/16.
Spending on health, schools and international aid will continue to be given protection.
Ministers are preparing for the spending review to be held on 26 June.
Chancellor George Osborne announced in last week's Budget speech that he wanted to cut another £11.5bn from public spending.
Danny Alexander, the Chief Secretary to the Treasury, wrote on Wednesday to ministers telling them that that would mean reductions of up to 10% from each of their budgets, on top of the savings they have already made.
Defence spending will be partly protected, with the Ministry of Defence's equipment budget rising by 1% above inflation. The rest of its spending will be cut by just 5%.
BBC deputy political editor James Landale said the figures were not final, but the Treasury's "opening gambit for negotiations in the weeks ahead".
A Treasury spokesman said: "The chief secretary has today written to departments to set their planning assumptions for the 2015/16 spending round. Setting planning assumptions is a normal part of the spending round process. These are planning assumptions that allow flexibility, not final decisions."
For Labour, shadow Treasury minister Chris Leslie said: "David Cameron and George Osborne never wanted or expected this spending review to happen.
"They said their plan would balance the books by the next election, but their failure to deliver economic growth means there is now set to be a deficit of over £90bn in 2015/16. That's the reason why the Treasury is now looking for even more spending cuts and tax rises."