Ken Boston said coursework would only be kept where it could be shown to be the most reliable way of ranking pupils. The move could bring to an end 20 years of coursework being a major part of many subjects.
A significant minority of Welsh schools opt for exams set by the English exam boards, so would be affected by the move.
John Valentine Williams, chief executive of ACCAC, the Welsh qualifications, curriculum and assessment authority, said its English counterpart was "working closely with its equivalent authorities in Wales and Northern Ireland on this issue".
Even in subjects where coursework is retained, schools would no longer be able to choose whether pupils did it or not, said Dr Boston. It would either be compulsory, for some elements, or unavailable.
Longer-term changes to GCSE could see a reduction in the amount of time pupils spend in the exam hall, as the Qualifications and Curriculum Authority reacts to concerns that young people are over-assessed.
Dr Boston's comments came in a TES interview. John Major, the former Conservative prime minister, forced exam boards to ditch 100 per cent GCSE English coursework in 1993 amid concerns it was a soft option for pupils.
Ruth Kelly, the Education Secretary, had asked the QCA to investigate scaling coursework down because of concerns about pupil plagiarism.
Keith Davidson, who chaired the group which drew up plans to introduce 100 per cent coursework to some English GCSEs in 1986, said "all hell would be let loose" if it was eliminated in that subject.
He said: "Scrapping coursework would be absolute anathema to a lot of English teachers. You cannot assess properly how pupils write in an examination room, because it is a totally artificial situation."
However, some teachers have complained about the workload involved. Others say coursework has become an exercise in getting pupils to "jump through hoops".
The QCA is beginning a consultation on Monday about the future of maths coursework, which will ask teachers whether GCSEs should be exam only.
Consultation on other subjects will follow. Change could be introduced for courses beginning in 2010. There is no prospect of subjects including art, music and design and technology becoming exam-only. But Dr Boston refused to rule out such a move in others, including English literature.