The move threatens the jobs of up to 45 staff at the Treasury, but if the service is contracted out they will be allowed to mount an in-house bid in competition with private sector economic forecasters.
The idea of contracting out the forecasting function was floated in late 1994 in a Treasury review of its own expenditure which has since led to a sharp reduction in the number of civil servants.
But at the time Mr Clarke decided to delay the detailed review of the forecasting function for a couple of years.
The three-month consultants' study is to look at the feasibility of contracting out the central economic forecast and the forecasting and monitoring of public finances.
Other areas would include the background work required to produce the economic assumptions made in public expenditure planning, and the assessment of the accuracy of forecasts, by looking at what happens in the economy.
The Treasury said that if the consultants' report confirmed that a "market test" was feasible, a formal contract specification would be issued in late spring or early summer inviting outside organisations - and Treasury staff, if they wished - to make bids.
The aim would be to complete negotiations in time for the successful bidder to take over responsibility for forecasting from the end of this year.
The Treasury said the study would include the security implications of allowing an outside organisation to have access to sensitive forecasting information that is a key part of the Budget announcement.
It would also examine options such as moving the forecasting function entirely outside the Treasury or having civil servants working alongside a private firm.
Comment, page 15