The company is already talking to at least three agencies, with a view to appointing one to develop a global relationship marketing strategy.
Agencies have been asked to develop a programme of communications to encourage patients to continue taking the drugs on a long-term basis.
Many patients stop taking the medicine after three months, once they see their cholesterol levels drop.
Crestor is available in the UK as a prescription-only drug and competes with Pfizer's brand Lipitor, the world's biggest-selling drug.
AstraZeneca, along with executives from the rival company GlaxoSmithKline, recently came out against the idea of the UK moving to the US model where advertisers are allowed to use above-the-line advertising to market prescription medicines. The companies felt that the public would be against such a move.