In this paper, we investigate the Ghost Dark Energy (GDE) and the Generalized Ghost Dark Energy (GGDE) in a cyclic universe in which the high-energy regime is modified by the effects of quantum gravity, causing a turnaround (and a bounce) of the universe. First, we study the non-interacting cases for both of these models. We find that, in the absence of interaction in a cyclic universe, the deceleration parameter becomes a constant; as a result, the universe cannot move from an accelerated expansion phase to a deceleration phase and so cannot reach turnaround point and starts to contract. Then, we extend our study to the interacting GDE and GGDE models. We obtain the evolution of the dark energy density, the deceleration and the equation of state parameters for these models in a cyclic universe. In this case, the transition from an accelerated expansion phase to the deceleration phase in the future (near the turnaround point) can be achieved in a cyclic universe.