Foster and Partners pitched for the scheme on its own, whereas Foreign Office was part of United Architects, a consortium of six practices. The other designers shortlisted for the project include Daniel Libeskind and teams led by US practices Richard Meier, Rafael Viñoly and Skidmore, Owings & Merrill.
The shortlisted teams were selected in October from 407 submissions to client the Lower Manhattan Development Corporation.
The LMDC launched the competition in the summer after an unenthusiastic response from New Yorkers to plans by US architect Beyer Blinder Belle.
A decision on designs for rebuilding work is expected to be made by the corporation at the end of January. It is also launching a separate design competition for a specific memorial on the site late next year.
The design teams' plans must include a range of commercial space, a grand promenade and a powerful skyline element.