Work is scheduled to start in 2012 on the 10,000 sq metre refurbishment project.
Up to five specialists will be shortlisted for the job and firms must express an interest by May 20.
The Bank is currently looking for new offices in the City which will be home to the new Prudential Regulatory Authority watchdog.
The offices will be bought as a shell and need to be completely re-fitted to make them fit for purpose.
For more details about the job and to apply visit www.bankofenglandtenders.co.uk