The proposal emerged from the council's response to the Scottish Executive's current review of the "age and stage" restrictions on when pupils can sit exams. Abolition of these regulations is one of five options the Scottish Executive is canvassing.
East Renfrewshire's suggestion is highly tentative - it would depend on the age and stage restrictions being removed, primary pupils would only take unit assessments, not the external exam, subjects would be confined initially to practical science and information technology, and consensus would have to be achieved among parents and others after consultation.
James McVittie, head of St Ninian's High in Eastwood, who chaired a council working group on the curriculum, reflected the caution: "We are saying that flexibility, progression, breadth and balance are the basis of a relevant and developing curriculum and that the concept of national certification at primary 7 is just one possibility.
"We are not saying it should take place or will take place, just that it is a possibility that may be examined."
A council spokesman said primary pupils in their final year were already working up to Intermediate 1 level. They were doing PowerPoint presentations at Mearns primary, he pointed out.
John Wilson, East Renfrewshire's director of education, said in his report to the council: "The overriding priority in formalising this curriculum framework is to meet the needs of the learner with more appropriate curriculum patterns which will improve pupil motivation, learning and attainment."
The working group was at pains to make clear that it was not advocating "a breaking free to a laissez-faire, anything goes approach to curriculum "planning". There had to be consistency and broad principles to guard against "the unfettered enthusiasms of individual headteachers".
Any changes following the Executive's decision on when pupils should be allowed to sit exams will also have to overcome concern in union circles, where fears have been expressed at the prospect of very young pupils being expected to sit national exams when they are not mature enough.
Mr McVittie's team makes a string of other recommendations covering the three stages for 3-5s, 5-14 and post-14. These include extending Standard grades National Qualifications to S2, the use of primary teachers in S1-S2 and secondary specialists in P6-P7 and certificating core skills in S2.
Meanwhile neighbouring Glasgow has not gone as far as East Renfrewshire but it is recommending the abolition of the current exam restrictions in their entirety, rather than merely replacing them with national guidance.
A report to councillors yesterday (Thursday) says this would open up the possibility of enabling schools to present candidates for Access 3 at S2, Standard grade at S3, Intermediate 1 at S3 and Intermediate 2 at S4. If, however, uptake was considerable, the cost could be substantial.