Gene regulatory networks (GRNs) play a crucial role in biological processes, with their dynamic behaviors heavily influenced by the spatial organization of genes. In particular, reaction-diffusion mechanisms govern the coupling between adjacent spatial locations in continuous time GRNs. However, traditional models often ignore the spatial coupling and reaction-diffusion properties of these networks, especially in discrete-time settings. In order to solve this problem, a new discrete-time gene regulatory network model is proposed in this paper, which explicitly considers the mutual coupling between adjacent spatial positions. To ensure the passivity of the proposed model, delay-dependent stability criteria are established by constructing appropriate Lyapunov-Krasovskii functions formulated in terms of linear matrix inequalities. To showcase the effectiveness and validity of this approach, a numerical example is presented in this paper. The results reveal that the model accurately captures the spatial coupling and reaction-diffusion nature of gene regulatory networks in discrete time settings.