The council's education committee agreed last week to establish a working group of officials, teachers and experts in the field to come up with proposals.
Douglas Academy, which houses the national school for gifted young musicians, is in East Dunbartonshire and the council sends four pupils there. Another four attend the national dance school at Knightswood Secondary in Glasgow.
Ron McInally, the council's education convener who will also serve on the working group, claims that based on examination results East Dunbartonshire has a higher than average number of more able children.
But a report by Ian Mills, director of education, cautioned that defining gifted or more able pupils was complex and went beyond exam performance. Talents in the arts and sport also had to be acknowledged.
Mr McInally stressed the policy was not about shifting gear in an elitist direction but was part of the council's commitment to develop the abilities of all pupils.