We investigate the nucleon generalized polarizabilities in virtual Compton scattering within a relativistic framework, defining such quantities through a Lorentz covariant multipole expansion of the scattering amplitude. The key physical ingredients in the calculation of the nucleon polarizabilities are the Lorentz invariant reduced matrix elements of the electromagnetic transition current, which can be evaluated from off-shell helicity amplitudes. The evolution of the proton paramagnetic polarizability, as a function of the virtual photon three-momentum transfer is explicitly evaluated within a relativistic constituent quark model by adopting transition form factors obtained in a light-front formalism. The discussion is focussed on the role of the relativistic effects and transition form factors, by comparing our model predictions with theoretical calculations based on different nucleon structure models.