Hundreds of thousands of public sector workers are reportedly in line to get a pay rise.
Most members of the armed forces will get a 2.9% rise, teachers and school staff 2.75%, police officers, dentists and consultants 2.5%, senior civil servants 2%, the Times said.
It is thought the rise will come from existing budgets.
The Treasury is expected to confirm the increases on Monday, in one of Theresa May's final acts as prime minister.
Senior members of the armed forces will receive a 2% rise.
The government will be responding to the independent pay review bodies, which recommend pay for many public sector workers.
The review bodies cover armed forces across the UK; police in England and Wales; school teachers in England, and senior civil servants in England, Scotland and Wales.
Doctors and dentists in England are also included, but GPs are subject to a separate pay deal.
The NHS pay review body also recommends pay for doctors and dentists in Wales, Northern Ireland and Scotland - but the devolved administrations will respond to this.
Public sector pay was frozen for two years in 2010, except for those earning less than £21,000 a year, and after that rises were capped at 1% - below the rate of inflation.
Theresa May continued the cap until last year when she announced austerity was coming to an end.
The rises do not apply to other public sector staff, such as more junior civil servants and nurses, the Times added. Their pay is dealt with separately.
Paul Johnson, director of the Institute for Fiscal Studies think tank, said the proposals were similar to pay rises implemented last year.
He told BBC Radio 4's Today programme that many of the pay increases were "only just" above inflation - which is currently at 2% - and were still slower than average pay rises in the private sector.
Both public and private sector workers have seen their average pay rising more slowly than prices since 2010.
Mr Johnson said it would be "difficult" to make the argument that funding would come from existing budgets - and therefore it would mean cuts elsewhere.
He said budgets for next year had not yet been set and he "would be surprised" if they do not increase.
BBC political correspondent Iain Watson said if the money were to come from existing budgets, cuts would have to be made elsewhere to fund the above inflation aspect of the pay increases.
"That is a big challenge for Theresa May's successor," he said. "Will they say the age of austerity is finished and fully fund them? Or will they say cuts will be have to be made virtually as soon as they take office?"
Pay rise 'not enough'
Anne, who teaches at a sixth form college, said the news of a pay rise was welcome but was not enough to make up for the impact of nine years of pay being capped.
"I'm fortunate because I'm not the main breadwinner, but in an area like Surrey, where I live, the cost of housing can be a real struggle for some teachers," she said.
If pay rises had to be funded out of existing budgets Anne said this would be "catastrophic" and make the job of teachers even harder at a time of stretched resources and growing class sizes.
"I am unconvinced that this move will make teaching a more attractive employment prospect," she added.
"There's still a real issue with recruitment. I work in a fairly big department but six of us are over 50, so who is going to replace us?"
Labour's shadow chancellor John McDonnell said the government's public sector pay offer was "insulting".
"After years of holding back the pay of our dedicated public sector workers, it is shameful for the government to pay for ending the public sector pay cap with more cuts," he added.
Gail Cartmail, assistant general secretary of the union Unite, said the pay rise would not "ease the wage pain of hard-up workers".
She added public workers "will not be fooled" by Mrs May's attempt to "curry favour with an austerity-hit workforce".
Instead, she called for "a properly funded pay rise which tackled the pay misery of the last nine years".
Rehana Azam, of the GMB union, described the pay rise as "smoke and mirrors".
"All of England's five million public sector workers deserve a proper pay rise after almost a decade of real-terms pay cuts - not just a select few," she said.
Joint general secretary of the National Education Union Kevin Courtney said the 2.75% pay increase for teachers was not enough and would see their pay fall further behind pay increases in the wider economy at a time of "a worsening recruitment and retention crisis".
"If the pay rise isn't funded in full this will mean more cuts to our children's education," he added.