We study dependence of jet quenching on matter density, using "tomography" of the fireball provided by RHIC data on azimuthal anisotropy v_{2} of high p_{t} hadron yield at different centralities. Slicing the fireball into shells with constant (entropy) density, we derive a "layer-wise geometrical limit" v_{2};{max} which is indeed above the data v_{2} < v_{2};{max}. Interestingly, the limit is reached only if quenching is dominated by shells with the entropy density exactly in the near-T_{c} region. We show two models that simultaneously describe the high p_{t} v_{2} and R_{A-A} data and conclude that such a description can be achieved only if the jet quenching is few times stronger in the near-T_{c} region relative to QGP at T > T_{c}. One possible reason for such enhancement may be recent indications that the near-T_{c} region is a magnetic plasma of relatively light color-magnetic monopoles.