The problem of non-Fickian diffusion in a two-component mixture at uniform temperature is studied in the framework of extended irreversible thermodynamics (EIT). The basic idea underlying this formalism is to complement the space of classical variables (here the mass density, mass concentration and barycentric velocity) by dissipative fluxes (here the diffusion flux). The evolution equation for this extra variable is derived by using the Lagrange multipliers method of Liu. After solving the problem in the case of the Linear regime, we extend our analysis to a non-linear situation. In the linear case, one recovers the classical Fick's law and the Cattaneo-Maxwell equation for the diffusion flux. In the non-linear case, our results are comparable with those obtained by using a Hamiltonian formalism.