  The four--quark system $c\bar c n\bar n$ is studied in the framework of the
constituent quark model. Using different types of quark-quark potentials, we
solve the four--body Schr\"odinger equation by means of the hyperspherical
harmonic formalism. Exploring the low laying $J^{PC}$ states for different
isospin configurations no four-quark bound states have been found. Of
particular interest is the possible four-quark structure of the X(3872). We
rule out the possibility that this particle is a compact tetraquark system,
unless additional correlations, either in the form of diquarks or at the level
of the interacting potential, not considered in simple quark models do
contribute.
