The interaction between hippocampal ripples and cortical slow oscillations (SO) has been proposed to play a critical role in memory consolidation during sleep. However, the neuronal mechanisms underlying the transmission of ripples within cortical regions remain poorly understood. In this study, we used a computational model to investigate how ripple events propagate through cortical networks. We found that sparse and weak inter-areal connections impede ripple propagation, while dense and strong inter-areal connections facilitate it. Notably, our findings reveal that when cortical networks exhibit slow oscillations (SOs), characterized by alternating up and down states, ripples occurring before the SO peak can propagate to distant cortical areas even in the presence of sparse and weak inter-areal connections. These results indicate that the precise coordination between SO and the ripple promotes efficient communication in cortical regions during sleep. This study offers new mechanistic insights into the role of SOs during slow-wave sleep, deepening our understanding of the processes underlying memory consolidation.