Brunel University wants to found a school to encourage disadvantaged students to enter higher education.
Vice-chancellor Steve Schwartz said: "We are looking for high-achieving pupils who could be lost in the system. If you really want to make an impact, you have to start early. There's an aspirational problem: many people think that university is not for them, so we saw this as a reach-out activity.
"The school would be located on a university campus where students get used to using, say, the sports facilities and the catering. In the sixth form, teaching could be in a university format: lectures and tutorials."
The plans, which could be extended to incorporate a primary school, are being discussed at the Department for Education and Skills, and the school could be set up in two years' time.
Professor Schwartz would like the school to be independent from the state. It would be sited on the university's Runnnymede campus. Brunel University staff would not be asked to teach pupils.
The school would not be the first to be established by a university. In 1830, University College London founded one that is now an independent boy's school in Hampstead.
Jordanhill School in Glasgow was founded in 1920 by the Jordanhill College of Education, now part of Strathclyde University, as its demonstration school. It is funded by a direct grant from the Scottish Executive.
In his previous role as vice-chancellor of Murdoch University in Australia, Professor Schwartz established Murdoch College, a private on-campus school. The school's website boasts that it shares access to university and college facilities, courses and resources.
Under the Partnerships for Progression initiative, the London region has been asked to get 45 per cent of young Londoners into higher education by 2010, up from the current level of 35 per cent.