Instead, 14 to 16-year-olds will only have to sit courses in communication and numeracy. English literature and the more academic maths topics will be optional.
The plan is a key element of detailed proposals, expected to be announced in the New Year, for a new diploma exam system which could replace A-levels and GCSEs in English schools within 10 years.
The taskforce, led by former chief inspector Mike Tomlinson, will also reject the possibility of forcing teenagers to study particular combinations of subjects in the sixth form.
The proposals are to be outlined in the second report of the taskforce's 18-month inquiry next month.
The group is seeking to put more emphasis on literacy and numeracy in the latter years of secondary school. It will propose that all students complete a course in basic numeracy and in communication, embracing reading, writing and speaking.
Most would also take more conventional English literature and maths courses.
But youngsters might be able to achieve an intermediate diploma at GCSE level, without completing these courses.
Currently, studying English and maths is compulsory under the national curriculum. The taskforce believes that the change it is proposing would re-engage thousands of youngsters.
It will take soundings on its plans before producing a final report for ministers to consider next summer.