The proposed development, which has been consulted on with the Council and English Heritage, will sit above an access shaft, which is a single storey structure providing access and ventilation to the Crossrail tunnels below ground.
The building will border a Grade II listed building on Southampton Row and has been designed to ensure the upper levels are set back to leave space between the new development and the existing listed building.
The Fisher Street scheme is part of Crossrail's plans for a total of 3 million square feet of office, retail and residential space to site above new Crossrail stations. It said in a statement that it has secured planning consent for nearly 1m sq ft so far.
"The Fisher Street plans offer a striking piece of architecture for a unique opportunity to deliver new residential space in a prime central London location," said Crossrail's land and property director Ian Lindsay.
"This is one of a number of commercial opportunities in the pipeline and we are continuing to seek new development partners to help us deliver a range of future schemes,” he said.
