The council wants to promote its accreditation for graduates who work with children aged 0-5 years.
Farm and Publicis have also been shortlisted by the COI to compete for the account.
The winning agency will be briefed with creating a campaign that includes TV, poster and online work, and highlights the benefits of the award to employers and prospective trainees.
Claire Hamilton, early years communications officer, said: "Early years professionals are already making a difference to the lives of children, but we want to make sure more people take up the status.
"We are looking for a creative idea that can translate across the media board and has the longevity required to support a three year campaign."
The council has already selected Arena BLM to handle media duties.
The CWDC was set up to improve the lives of young people, their carers and families by ensuring everyone who works with them has the best possible training, qualifications, support and advice.
The first early years professionals were accredited in February 2007 and currently 1,700 people have successfully achieved the status.
By 2015, the government plans to have an EYPS-qualified worker in every day-care setting. Recent research carried out by the CWDC shows that the sooner qualified helpers are involved with children, the better their educational outcome.