There has been a row brewing at Westminster for some time over cuts to so-called Short money.
But sources are confident MPs will back a plan that will save 10% from the total in a vote expected on Wednesday.
Ministers say Short money payments are unduly generous given cutbacks elsewhere in the public sector.
In November, George Osborne's Autumn Statement revealed plans to cut the funding - named after former Labour MP Ted Short - by 19%, saying this would be in line with savings expected of unprotected Whitehall departments.
The plans have been strongly criticised by opposition parties.
The proposed compromise would shift the formula for calculating the payments from taking account of the Retail Price Index to instead using the Consumer Price Index.
Over the last 12 months the CPI has grown by a far smaller rate than the RPI - so the switch makes the new formula less generous.
It will necessitate what a source described as "much greater transparency" over what the money is spent on.
In addition, it will set a floor below which Short money cannot fall for the smallest parties in the House of Commons - those with between one and five MPs.
That floor is Â£75,000 a year. There is also a ceiling for those parties, of just over Â£200,000.
Between now the end of the decade sources claim the compromise arrangement will save the taxpayer around Â£3.5m.
Commons sources say the government is to propose a compromise deal on the funding opposition parties are entitled to - and put it to a vote next week.