A principal element of strongly interacting matter phenomenology is the quark confinement at low baryonic densities. We develop an approach based on the relativistic density functional motivated by the string-flip model, which provides the low density suppresion of quarks due to rise of their self-energy already at the mean-field level. Dynamical restoration of chiral symmetry is ensured by construction of the density functional. The connection of the present approach to the Nambu-Jona-Lasinio model with density dependent coupling constant is demonstrated. Supplemented with the vector repulsion and diquark pairing channels it is applied to model a cold quark matter. We also use the corresponding equation of state for modelling compact stars with quark cores.