Education Secretary David Blunkett made the commitment at last week's Labour party conference, announcing a Pounds 500 million package aimed at cutting truancy and exclusion rates by a third in three years.
Part of the new "pupil support grant" will be paid to all education authorities. But the Local Government Association is worried it will not be enough.
Neil Fletcher, the LGA's head of education, said: "We are looking for more information about how provision for excluded pupils is going to be funded. We would be very concerned if it meant education authorities paying a larger proportion.
"We were thinking that Pounds 10,000 per pupil might not be unrealistic for the kind of specialist attention these pupils are going to need." All the pupil support grant - part of the Government's standards fund - is based on matched funding. Labour has set aside Pounds 22m in 19992000 for excluded pupils, half of which will have to come from local authorities.
Assuming last year's figure of 12,700 permanent exclusions remains steady, that works out at a very approximate Pounds 1,730 extra per pupil per year. The cost to education authorities of excluded pupils has been estimated at Pounds 5,000.
A Department for Education and Employment spokesman said increasing sums of money would be available in 200001 and 200102, when exclusions should also be declining.
The rest of the new grant - Pounds 37m in 19992000 - will be allocated by competitive bid, with around 110 authorities expected to win additional funding for preventative work, ranging from pupil mentoring to staff training. Some of this funding will be targeted at schools with many "at risk" pupils.
Councils seeking a share of the new cash will have to show how they are improving the attainment of children in care - whether or not their proposals target such pupils.
David Blunkett wants to "prick the conscience" of local authorities over children in care, who are 10 times more likely to be excluded from school than average.
But there is no similar requirement for other high-risk exclusion groups, such as African-Caribbean boys or children with special educational needs.
Sir Herman Ouseley, chairman of the Commission for Racial Equality, has previously criticised the Government's social exclusion unit for not setting targets for reducing ethnic-minority exclusion rates.
But a DFEE spokesman said the requirement to report on children in care would not determine funding. Bids targeting any or all three "at risk" groups were welcome.