As well as his COI role, Bishop is currently acting permanent secretary for Government communications. He is standing in for Howell James while a permanent replacement is sought.
The news means that Bishop is out of the running to be the next permanet secretary for comms - although insiders have previously said that Bishop was not interested in the job on a permanent basis.
The Cabinet Office has a shortlist of four for the permanent secretary role, who will all be seen by a panel of interviewers in the coming month.
The COI has no news yet on a replacement for Bishop, adding that the recruitment process will be handled by the Cabinet Office.
In the new role, Bishop, a former chairman of Saatchi & Saatchi International, will replace Michael Lynch, who leaves in April 2009.
