The move will be seen as an embarrassment for the Qualifications and Curriculum Authority, which stood by the controversial tests earlier this year.
This week the body revealed that it is to launch a consultation over wholesale changes to the Shakespeare exam, which is taken by 600,000 14-year-olds every year.
The changes, which would be introduced in 2005, could include bringing the assessment of Shakespeare forward to the spring term to reduce the testing burden on schools and allow the exam to fit in with school timetables. It would also ease the pressure on markers.
However, this would mean moving the shorter writing task from the Shakespeare paper to the writing paper, with the longer writing task.
This part of the test is connected to a theme or issue from a play but it has been criticised for having too tenuous a link with the text and for confusing pupils, who were not sure what was expected of them.
If the writing task is moved then the Shakespeare test would consist of just a 45-minute reading task, which QCA chiefs believe could be taken in lesson time.
However, the QCA states it would have to consider the cost of sending out separate delivery of tests and information to examiners in spring.
A letter accompanying the questionnaire states that "some issues have arisen on which we would like to sound out opinion".
It is being sent to a representative sample of schools, all local authorities, teaching unions, as well as teacher and subject organisations.
The Shakespeare test led to a heated debate earlier this year when it was revealed that pupils could gain more than half of the available marks without having to actually read a word of the Bard's works.
The test taken last May allocated 18 of the 38 marks to questions testing the understanding of two scenes from either Henry V, Twelfth Night or Macbeth.
However, the writing element, which was worth 20 marks, merely gauged candidates' linguistic and grammatical skills and required no knowledge of the plays, critics said.
Dr Bethan Marshall, of King's College London, condemned the paper as a "ghastly attempt to make Shakespeare more contemporary".
Further attacks on the rigour of the exam from teachers prompted the Education Secretary Charles Clarke to demand explanations from the QCA.
At the time the QCA said that the tests had been approved by Mr Clarke's predecessor Estelle Morris "following extensive consultation" and there were no plans to change them.
Later, however, Ken Boston, QCA chief executive, admitted they needed to be looked at again.
The deadline for the consultation is November 3.