Schools are already expected to promote well-being
Schools in England could be made to keep records of pupils' drug use and obesity under plans being considered.
A discussion document seen by The Guardian details how 18 aspects of pupils' lives, including the incidence of pregnancies, could be monitored.
The idea was first set out in the Children's Plan published by the government last year.
Head teachers, now being consulted over the plans, said it would be "absolutely wrong to dump this agenda on schools".
Schools have had a duty to promote the broader well being of their pupils since 2006 - for instance by encouraging them to exercise and eat healthily.
In the Children's Plan, ministers said England's schools' inspectorate Ofsted should judge schools on pupil well-being as well as exam results, exclusion rates and other existing factors.
The discussion document gives more details, suggesting bullying, obesity, entrance to the youth justice system, and destinations on leaving schools could also be included, according to The Guardian.
Ofsted could begin monitoring such areas as early as next year.
John Dunford, general secretary of the Association of School and College Leaders (ASCL), said: "Children only spend a small proportion of their lives at school. It's absolutely wrong to dump this agenda on schools.
"Schools have a part to play in reducing obesity and in reducing teenage pregnancy but that has to be part of a whole area strategy. It's not something you can measure each school against."
The Association of Teachers and Lecturers says teachers should not be held responsible for all aspects of pupils' lives.
Mary Bousted, the union's general secretary, said: "If the government adds more targets over which schools have very little control that would sound the death knell for teachers and school leaders.
"While it's important for schools to have good joined-up working with a range of other services, they can't be held responsible for everything."
Schools Minister Jim Knight said Ofsted had been evaluating schools' contribution to children's well-being since 2005.
"Schools have a crucial role to play in children's lives but it is not down to them to solve issues in wider society alone - and we have never said it was. We want teachers to be able to focus on teaching.
"In the Children's Plan we announced that we want to do more to ensure schools get the support needed for pupils by bringing integrated services into schools. It is about schools being able to tap into expert outside help.
"It will simply focus inspections on how children's lives are improving and we are discussing with schools, unions and local authorities how we can make sure this can be assessed more fairly, recognised and properly rewarded."