, edX president Anant Agarwal said this could include courses designed by individual schools.
"If a school has the resources to create good-quality online courses, and has a similar mission to us, then absolutely," he said. "I am personally deeply committed to this because how can students benefit from high-quality college courses if they don't have the background from high school?"
The Mooc phenomenon has expanded rapidly in the past six years. Significant players such as edX were established by leading universities after initial experiments in offering free online courses and lectures attracted huge numbers of learners from around the world.
Dr Agarwal said that edX, which is still predominantly university-based, already had 100,000 high school students among its 2 million learners. Young people's familiarity with the online world meant they were "absolutely ready" for school-based Moocs, he said.
Speaking at the Global Education and Skills Forum in Dubai earlier this month, he added: "Why are we dragging them to class and making them sit through one-hour lectures?
"In a Mooc, we replace the one-hour lecture with learning sequences of short five-, 10-minute videos just like YouTube, interwoven with engaging interactive exercises, much like the video games kids play. It is much more engaging."
At the conference, edX announced that it was entering into a deal with Gems Education, an international chain of private schools, to develop high-school-level courses. Marc Boxser, director of strategic initiatives at Gems, said that the company was considering basing its courses on the "British curriculum", the International Baccalaureate (IB) or the Indian Certificate of Secondary Education.
But the move to include individual schools is likely to create new opportunities, especially for institutions that already have well-established reputations.
William Richardson, general secretary of the Headmasters' and Headmistresses' Conference, which represents leading British private schools including Eton College and Harrow, said the idea would attract his members. "All schools are interested in putting up excellent content for anyone to use, particularly colleagues in other schools," he said. "They do want to share.
"This is about putting up courses for public benefit and drawing attention to your school as the creator of the material."
In some ways, Moocs could suit the schools system better than universities. Higher education courses differ hugely from institution to institution, but exams and national curricula mean that school courses are often already standardised.
Schools that could offer courses for popular international qualifications such as the IGCSE could be well-placed to benefit, although they would not be able to charge directly for their material. "The courses are free to learners," Dr Agarwal explained. "But we do have some revenue models where we charge for certificates and we do a revenue share with the producer of the course."
Asked whether schools could make money from certificates, he said: "It is difficult to say. On the internet, quality rises to the top. People have a way of finding things and a lot of unknown names have become stars on the internet."
In the past, entrepreneurial schools have made large amounts of money from offering their courses online. Thomas Telford School, a state school in Shropshire, England, raised millions in the early 2000s by selling vocational ICT courses.
The online potential of the IB has already been spotted by Pajoma Education, a social enterprise set up by a group of Swiss-based financiers. It intends to make the entire IB Diploma Programme available through live online lessons from September, although it will charge.
John McCall MacBain, founder of Pajoma Education, said that such schemes could improve the quality of teaching and bring the international nature of the world's leading universities down to school level. "Our classroom will be 20 or 30 students from 10 different countries interacting with a teacher who probably isn't the [same] nationality," the philanthropist told the forum in Dubai.
But he called on governments to ensure that students were safe. "We need supervision that we don't think of at the university level," he said. "Where are these children going to take their courses? I think the regulation should be thorough."