The housing project, designed by PRP Architects, is a mixture of affordable and private housing.
A source at one of the three firms said the job could lead to more housing work on the 17 ha site. The source said: "It could mean staying on that site for quite some time."
Quintain submitted outline planning permission for the scheme last October to Brent council. It also includes offices, shops, a cinema and a £20m refurbishment of Wembley Arena. The project has been masterplanned by Richard Rogers Partnership.