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The development of an efficient and accurate numerical method, able to capture the very thin concentration boundary layer in cases of interfacial mass transfer at fluid interfaces in two-phase systems, is a challenging task. In this study, a meshless finite-difference method based on radial basis functions has been adopted. The use of radial basis functions has proven to be helpful in multidimensional problems with complex geometries, in which the use of scattered sets of nodes is preferable. Unlike most of the applications reported in literature, the proposed method has been employed in two-phase flows, with two regions connected by a surface, i.e., the fluid interface, on which additional boundary conditions have to be fulfilled. Two validation test cases with increasing complexity are presented.