Sir Robert Smith, who set up the schools-business alliance, The Smith Group, was addressing what he described as the "scandal" of about 35,000 young people not in education, employment or training (Neet).
He said: "Could schools maybe own these people up to the age of 18, so that we can actually find out what happens?"
Sir Robert was speaking at a conference in Glasgow last week, organised by Learning and Teaching Scotland with The Smith Group and the Convention of Scottish Local Authorities.
Other speakers also argued that keeping better track of young people was crucial.
Graham Donaldson, senior chief inspector of education, said his organisation was altering how it inspected schools. Inspectors would look more closely at individual pupils, including those not present at the time of inspection.
He added that HMIE was looking at evaluating the transition from school to college more directly, and that an integrated approach to inspections was due by 2008.
Graham Short, East Ayrshire Council's head of education and social services, stressed the need for more information about the Neet group. He felt that there was little in the way of hard data and that existing statistics needed to carry a "health warning". "I feel I should know much more about this population than I do," he said.
Calum MacLean, Careers Scotland employment services manager, explained in a seminar how school leavers in Inverclyde had been encouraged to think about future employment. He described how a project called "Activate" had been used with S4-S6 leavers at two schools; it places importance on continuing to provide support to young people after they leave school. "You can't put people through these programmes, then just drop them," he said.
One of the conference's most remarkable presentations was made by Romany youngsters from West Dunbartonshire. Although Romany children can do well at primary school, their parents often withdraw them from secondary because of fears that they will face bullying and discrimination.
Members of the Romany Youth Action Group - made up of about 10 West Dunbartonshire youngsters aged 12 to 19 - explained how their weekly meetings had helped build confidence, and how they had stayed in formal education by attending cookery classes at Clydebank College.
One girl said: "None of us had ever imagined going to college. At first, we attracted a lot of attention - some good and some bad. As well as learning how to cook, we also learned a lot of other things."
Sir Robert described Neet as one of the "most intractable problems", pointing out that next year another 15,000 people would join the group. "If it is unsolved, it will have long-term negative consequences for the youngsters, and for society and our economy," he said.
"Solving it will bring glittering prizes for our society and economy, but most of all in terms of youngsters developing long-term employability, self-confidence and self-worth."