To quantize a coisotropic submanifold C of a Poisson manifold X means to consider star-products for wish the vanishing ideal I of C is a left ideal of the deformed algebra. We want to explain how such a construction is a byproduct of a formality conjecture a la Tamarkin. To this end we will describe a space of compatible multivectorfields quasi-isomorphic to cochains compatible with C. We will also discuss "obstructions" to this formality conjecture to hold.