The One Bedford Avenue building plans were drawn up by Bennetts Associates, and will see the old Time Out magazine building demolished to make way for the eight storey block on the lower east side of Tottenham Court Road.
Sir Robert McAlpine and Mace are understood to be among several firms eyeing the mixed-use development.
Exemplar are currently building Fitzroy Place on the site of the former Middlesex Hospital which Sir Robert McAlpine is due to complete by September 2014.