Pupils would be taught about pornography and sexting in all schools under new plans being drawn up by the government.
The proposals could be included in amendments to the Children and Social Work Bill, which is currently before parliament.
The chairs of five different Commons select committees recently called on education secretary Justine Greening to make SRE a statutory subject.
Their demand came after a report from the Women and Equalities Committee found that sexual bullying is now endemic in schools.
Currently free schools and academies do not have to teach sex education or personal, social, health and economic (PSHE) education. Parents can withdraw their children from sex education classes.
A government source told the Sunday Times: “Justine is clear that this is something that has to be looked at. It is not just a question of making it mandatory but also of what we should be teaching, including issues such as sexting and domestic violence.”
It is understood that it is now a priority area for Ms Greening and proposals have been drawn up.
A spokesman for the Department for Education said: “High-quality education on sex and relationships is a vital part of preparing young people for success in adult life – helping them make informed choices, stay safe and learn to respect themselves and others… we are actively looking at options to ensure that all children have access to high-quality teaching of these subjects.”