Ministers believe that the plan will circumvent EU rules preventing state aid to commercial enterprises because it does not involve direct payments to farmers.
Franz Fischler, the EU Commissioner for Agriculture, is expected to agree the deal next week. The plan has been worked out by the Scottish Rural Affairs Department, whose minister, Ross Finnie, met Nick Brown, the Minister for Agriculture, Fisheries and Food, and persuaded him of the need for intervention.
Mr Brown invited Mr Finnie to submit a scheme for the UK which is now being examined by ministers in Westminster, Scotland, Wales, and Northern Ireland before submission to Brussels. Nearly one fifth of the sheep population is in Scotland, where the problem is most severe. Farmers had been threatening to kill sheep and bury them. The price of two-year- old ewes, at pounds 7, is less than a quarter of what is was in 1997.
About 200,000 sheep would be involved in the Scottish cull but it remains unclear whether the funding would come from central funds in Westminster. As the problem is less severe in England and Wales it may be that the Scottish taxpayer would have to fund the scheme north of the border.