We study quantum entanglement of a system of spinless fermions itinerant in a lattice from a second-quantized perspective. The concurrence between any pair of local fermionic modes are analytically obtained for all the eigenstates of the system. Thermal entanglement in the grand-canonical ensemble is studied as a function of temperature and lattice filling. Relation between entanglement and superconducting correlations is discussed also for a BCS-like model.