In these proceedings we summarize the current status of the study of the sensitivity of the Cherenkov Telescope Array (CTA) to detect diffuse gamma-ray emission from the Perseus galaxy cluster. Gamma-ray emission is expected in galaxy clusters both from interactions of cosmic rays (CR) with the intra-cluster medium, or as a product of annihilation or decay of dark matter (DM) particles in case they are weakly interactive massive particles (WIMPs). The observation of Perseus constitutes one of the Key Science Projects to be carried out by the CTA Consortium. In this contribution, we focus on the DM-induced component of the flux. Our DM modelling includes the substructures we expect in the main halo which will boost the annihilation signal significantly. We adopt an ON/OFF observation strategy and simulate the expected gamma-ray signals. Finally we compute the expected CTA sensitivity using a likelihood maximization analysis including the most recent CTA instrument response functions. In absence of signal, we show that CTA will allow us to provide stringent and competitive constraints on TeV DM, especially for the case of DM decay.
