The campaign also aims to make it easier for young children to write to the prime minister.
It is understood that the Cabinet Office has already shortlisted two agencies from COI's roster but is looking for a third, non-roster agency.
The Government already produces an educational pack for secondary-school pupils.
The news emerges as the Government comes under attack from the shadow cabinet minister Chris Grayling for its spending on advertising.
COI's annual accounts show that total adspend rose by £14 million to £203 million in 2004 to 2005.
Grayling said research had shown that the Government has spent £67.2 million on advertising in the first three months of this year, more than any other advertiser.