The four-component relativistic Fock space coupled cluster method is used to describe the magnetic hyperfine interaction in low-lying electronic states of the KCs molecule. Both diagonal and off-diagonal matrix elements as functions of the internuclear separation R are calculated within the finite-field scheme. The resulting matrix elements exhibit very weak dependence on R for the separations exceeding 8 Å, whereas in the vicinity of the ground-state equilibrium the deviation of molecular HFS matrix elements from the atomic values reaches 15%. The dependence of the computed HFS couplings on the level of core correlation treatment is discussed.