The centre is based within a listed building, owned by Camden council, and offers support to young people who are homeless, vulnerable or at risk in King's Cross.
The project calls for the designs to be 'transformational and imaginative yet practical, addressing the constraints of the centre's occupation on the lower levels of the building.'
The statement added: 'The winning entry should unlock the potential within the centre, which is as yet unrealised.'
The scheme is being backed by Channel 4 newscaster and New Horizonchair Jon Snow.
He said: 'Our centre has to combine a sense of 'a safe place to be', privacy for one-on-one working for staff, and public areas for art, games, computing, cooking and eating.
'This competition holds out the hope for a use of our existing space that revolutionises the way we can work with those who depend upon our services. Architecture transforming life-prospects - could one ask for more?'
The competition is being funded by the John McAslan Family Trust, and is open to young architects as well as students.
The competition brief can be downloaded at www.ribacompetitions.comfrom the week commencing 16 October.