Universal free entitlement, funded by the States, started in January this year and so far 565 children have accessed it.
But Education, Sport & Culture said using figures from the Greffe of the number of three- to four-year-olds who are due to start school in September, it believed 3.6% were not taking up the offer.
However, a small number of those would be taking up the entitlement for the summer term, it said.
The cost for the spring term of the funded places was £592,827 – a cost of £1,049.25 per child, per term.
'Based on figures from the Greffe of the number of pre-school aged children of the correct age, we believe there are currently 21 children (3.6%) in the Bailiwick not accessing pre-school,' said an Education spokesman.
'The States Early Years Team (SEYT) is currently processing payments to providers for the summer term and is aware of a small number of additional children who will be taking up the entitlement after the Easter break.'
The current pre-school entitlement of 15 hours a week of free pre-school education is for 38 weeks a year (term-time) for all three- to four-year-olds in the year before they start school started in January 2017.
The current scheme, which has been referred to as a trial, has been extended for another academic year from September. This is in order to gain further evidence and information over its overall impact.
