The Corporation of London, which owns the Capital’s central criminal court, is due to announce the winner shortly.
Sources close to the project tip Interserve to take the decade-long refurbishment programme, which will concentrate on upgrading old boiler rooms and building services throughout the building.
Interserve has been up against Mitie and Skanska for the job, which was originally estimated to cost £60m but, has been scaled back to around £37m.
The contract to upgrade the Old Bailey will be phased to allow the 18 criminal courts to continue to operate during the modernisation programme.
Two of the courts at a time will be out of action and much of the work will be done at night to avoid disrupting trials.
The City of London Corporation will pay £27m, with the rest of the £37m bill paid by Her Majesty’s Courts and Tribunal Service.
The new boilers will be housed in the old coal cellar – a cavernous chamber deep underground with a hatch at one end leading down to the River Fleet – which runs under the building and down to the Thames.