In the drying process of polymer solution droplets, we propose an experimental procedure for visualizing the solute concentration profile by combining the fluorescent microscopy with the lateral profile observation. We have conducted a dynamical observation of the transport process of the solute polymer toward the edge that causes the "coffee stain phenomenon". We have found that the polymer concentration increases sharply near the edge, while it remains almost constant in the central region until the last stage of drying. The method is useful to understand the dynamical process that occurs near the contact line.