Business secretary Vince Cable is said to have been the last to reach a deal for his department ahead of the review, being announced to the House of Commons on 26 June.
Mr Cable is also reported to have secured one of the lowest cuts of the non-protected departmental budgets, at nearer to 8 per cent than the 10 per cent forecast.
This could mean the department having to save closer to £1.1 billion rather than the £1.4 billion previously thought. Together departments are being asked to find cuts worth £11.5 billion.
However, where the cuts will come from remains uncertain. As Times Higher Education reported last week, ministers look likely to abandon plans to find £875 million in savings by moving medical research and education budgets to the Department of Health; although a partial transfer remains a possibility.
If the proposal is dropped, it would raise the prospect of deeper cuts for higher education and the possible slashing of the National Scholarship Programme.
After George Osborne, the chancellor, announces each department’s settlement for 2015-16 on Wednesday, chief secretary to the Treasury, Danny Alexander, will announce detailed, longer-term plans for infrastructure spending on June.
Earlier this month Mr Osborne said that he hoped at the spending review to set out “the long-term commitment to science not just…the science budget for the year 2015-16”, raising speculation that science investment might form part of the infrastructure package.