We study the effect of viscoelasticity on the transportation of neutral solutes through a porous microchannel. The underlying transport phenomenon, modelled using the simplified Phan-Thien-Tanner constitutive equation, is actuated by the combined influence of pressure gradient and electroosmosis. Here, we obtain the closed form solution for the velocity distribution inside the flow domain and calculate the concentration profiles of the neutral solutes within the mass transport boundary layer by invoking the similarity solution approach. To establish the efficacy of viscoelastic solvents in the transportation of neutral solutes, which may find relevance in transdermal drug delivery applications, here we show the variations in the local solute concentration, the length averaged solute concentration at the wall, and the Sherwood number with the viscoelastic parameter. The present study infers that the shear-thinning nature of the viscoelastic fluid enhances the convective mass transfer as well as the permeation rate in the porous membranes. A complex interplay between the fluid rheology and the porous structure of the walls influenced by the electrochemistry at the interfacial scale modulates the mass transfer boundary layer of neutral solutes, implicating an effective method of mass transport in transdermal drug delivery applications.