A spokesman for the regulator confirmed Andrew Wright, who has been acting chief executive since Alistair Buchanan stepped down in June, is not applying for the permanent position.
Applications for the post, which attracts a salary of £190,000 and bonus of up to £15,000, closed on 7 October.
Information on the appointment has been closely guarded but industry sources have named a couple of potential external candidates.
One is Sarah Chambers, director of consumer and competition policy at the Department for Business, Innovation and Skills. She headed up postal regulator Postcomm between 2004 and 2008.
Another is Iain Osborne, group director of regulatory policy at the Civil Aviation Authority. He has prior industry experience as director of supply at Ofgem and chief executive of the Northern Ireland Authority for Utility Regulation.
With Labour threatening to axe the regulator and mounting political pressure from all sides, the role is seen as something of a poisoned chalice.
On Tuesday, Wright defended Ofgem against charges it was “feeble”, “seriously defective” and a “toothless tiger” before a select committee of MPs.