The backers want to construct a 400-unit building for key workers and the long-term homeless. As in the US version, the scheme will incorporate a retail element and healthcare facilities.
Project observers expect the consortium to acquire a site near Euston Road or the Elizabeth Garrett Anderson hospital, both in central London.
The Commission for Architecture and the Built Environment has been working on design guidance for the project. A King's Fund spokesman confirmed that an advertisement launching the competition will be issued on 22 November.
The development will be the first in Britain to house key workers and the long-term homeless.