The figure comes in a draft policy document which was due to be published earlier this month but has been held over until after the local elections on 4 May.
A leaked copy of the document discloses that the government's goal of recovering, recycling or composting more domestic waste could impose 'additional costs' of between£1.6bn to£2.8bn over the next 20 years.
But the government is not planning to provide extra funds to help councils meet the new targets.
But a letter from Michael Meacher, environment minister, to the secretary of state for the environment, John Prescott, said: 'Even without public funds, I am confident that we will be able to secure sufficient private sector funding for it to be active in each of the areas described in the waste strategy over its lifetime.'
The government will tell councils to reduce municipal waste dumped in landfill sites by 45% by 2010. They will also be expected to meet new targets for recycling or composting 30% of household waste.
The strategy will allow households that dump fewer rubbish bags to claim 'performance rewards' which can be traded for council services such as entrance to the local swimming pool.
The government plans to allow councils to 'trade' permits to dump waste if they have not filled their quotas.
The DETR said it was required to delay publication of the plans until after the local elections because the paper had an effect on councils.