Geological Carbon Sequestration (GCS) in deep geological formations, like saline aquifers and depleted oil and gas reservoirs, brings enormous potential for large-scale storage of carbon dioxide (CO2). The successful implementation of GCS requires a comprehensive risk assessment of the confinement of plumes at each potential storage site. The accurate prediction of the flow, geochemical, and geomechanical responses of the formation is essential for the management of GCS in long-term operations because excessive pressure buildup due to injection can potentially induce fracturing of the cap-rock, or activate pre-existing faults, through which fluid can leak. In this study, we build a Deep Learning (DL) workflow to effectively infer the storage potential of CO2 in deep saline aquifers. Specifically, a reservoir model is built to simulate the process of CO2 injection into deep saline aquifers, which considers the coupled phenomenon of flow and hydromechanics. Further, the reservoir model was sampled to account for a wide range of petro-physical, geological, and operational parameters. These samples generated a massive physics-informed simulation database (about 1500 simulated data points) that provides training data for the DL workflow. The ranges of varied parameters were obtained from an extensive literature survey. The DL workflow consists of Fourier Neural Operator (FNO) to take the input of the parameterized variables used in the simulation database and jointly predict the temporal-spatial responses of pressure and CO2 saturation plumes at different periods. Average Absolute Percentage Error (AAPE) and coefficient of determination (R2), Structural similarity index (SSIM), and Peak Signal to Noise Ratio (PSNR) are used as error metrics to evaluate the performance of the DL workflow. Through our blind testing experiments, the DL workflow offers predictions as accurate as our physics-based reservoir simulations, yet 300 times more efficient than the latter. The developed workflow shows superior performance with an AAPE of less than 5% and R2 score of more than 0.99 between actual and predicted values. The workflow can predict other required outputs that numerical simulators can typically calculate, such as solubility trapping, mineral trapping, and injected fluid densities in supercritical and aqueous phases. The proposed DL workflow is not only physics informed but also driven by inputs and outputs (data-driven) and thus offers a robust prediction of the carbon storage potential in deep saline aquifers with considering the coupled physics and potential fluid leakage risk.