Sub-nanolitre droplets engineered in microfluidic devices constitute ideal microreactors to investigate the kinetics of chemical reactions on the millisecond time scale. Up to date, fluorescence detection has been extensively used in chemistry and biology to probe reactants and resultant products within such nanodroplets. However, although fluorescence is a very sensitive technique, it lacks intrinsic specificity as frequently fluorescent labels need to be attached to the species of interest. This weakness can be overcome by using vibrational spectroscopy analysis. As an illustrative example, we use confocal Raman microspectroscopy in order to probe the concentration profiles of two interdiffusing solutes within nanolitre droplets transported through a straight microchannel. We establish the feasibility of the experimental method and discuss various aspects related to the space-time resolution and the quantitativeness of the Raman measurements. Finally, we demonstrate that the droplet internal molecular mixing is strongly affected by the droplet internal flow.