We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with Δℓ=1. We proceed in two steps. First, assuming that the only possible contaminant comes from our galaxy, we build an estimator using an azimuthally symmetric galactic mask for which analytical construction is possible. Applying this estimator to the V and W bands of the Wilkinson Microwave Anisotropy Probe (WMAP) data, we found an apparent detection in the V band. Further investigation of the foregrounds and the use of the kp0 mask provided by the WMAP team shows that, when the main extragalactic sources are properly removed, no significant detection remains.