Professor Barber's job as head of the Standards and Effectiveness Unit is advertised in this week's TES at a salary of at least pound;90,000.
The Department for Education and Employment is making the post into a permanent civil service position.
A week ago the first political adviser made the leap to becoming a career civil servant.
Michael Barber, who is classed as an expert adviser, is strongly associated with New Labour, but if he is successfully reappointed he will no longer be able to do political work for the party.
A long-standing member of the Labour party, he stood for Labour against Michael Heseltine in Henley in 1987. He was education chairman of inner-city Hackney and spent eight years at the National Union of Teachers.
In 1997 he was seconded to the DFEE from London University's Institute of Education on a rolling contract to head the standards and effectiveness unit, a role that would normally go to a career civil servant.
The unit is intended to be the DFEE's engine for school improvement, identifying good practice and focusing on raising standards.
It has been responsible fo co-ordinating the implementation of the national literacy and numeracy strategies as well as introducing new policies for raising standards in the early secondary years. It has also launched a number of new initiatives such as Education Action Zones, Beacon Schools and Excellence in Cities and the controversial Fresh Start.
Professor Barber, a regular TES columnist, is the only head of department at the DFEE who is not a civil servant and not on a permanent contract.
The successful candidate will be governed by the strictly non-partisan code of the Civil Service and will start work in December.
The job will be awarded after open competition and the selection will follow normal civil service procedures. It has already been advertised internally in Whitehall.
Earlier this month a political adviser to the Prime Minister became the first political appointee to become a civil servant. Geoff Mulgan, co-founder of the left-of-centre think-tank Demos, was appointed as the new director of the Cabinet Office's Performance and Innovation Unit, which oversees government policy and strategy. He was previously a political adviser in the Downing Street Policy Unit.