An approach is proposed to calculate Generalized Parton Distributions (GPDs) in a Constituent Quark Model (CQM) scenario, considering the constituent quarks as complex systems. The GPDs are obtained from the wave functions of the non relativistic CQM of Isgur and Karl, convoluted with the GPDs of the constituent quarks themselves. The latter are modelled by using the structure functions of the constituent quark, the double distribution representation of GPDs, and a recently proposed phenomenological constituent quark form factor. The present approach permits to access a kinematical range corresponding to both the DGLAP and the ERBL regions, for small values of the momentum transfer and of the skewedness parameter. In this kinematical region, the cross sections relevant to deeply virtual Compton scattering could be estimated by using the obtained GPDs. As an example, the leading twist, unpolarized GPD H has been calculated. Its general relations with the non relativistic definition of the electric form factor and with the leading twist unpolarized quark density are consistently recovered from our expressions.Further natural applications of the proposed approach are addressed.