Multiphase flows undergoing phase change are found in many environmental and industrial contexts, such as cloud formation and rainfall, cooling towers and spray combustion. These systems are inherently complex, with the different phases exchanging mass, momentum and energy through an interface that moves and deforms with the flow. Moreover, many flows of engineering interest exhibit compressibility effects, even if the flow velocities are relatively small and much smaller than the speed of sound in extended regions of the domain. Labelled as low-Mach flows, these types of flows share characteristics with both the fully compressible regime and the fully incompressible regime, making their numerical simulation challenging. In the current study we propose a novel methodology which has the potential to simulate low-Mach flows undergoing phase change. This approach utilizes an Eulerian mass- conserving diffuse interface model for solving the gas-liquid interface [1], applied to a low Mach number multiphase model for flows composed of liquid and a gaseous component consisting of vapor and inert gas. Coupled with this, we employ a consistent scalar transport equation, thereby reducing the necessity for imposing specific boundary conditions at the interface [2]. This not only enhances the efficiency of our work but also reduces its overall complexity. Interfacial mass transfer is modeled via chemical potential relaxation source terms that drive the liquid and vapor phases towards equilibrium. The proposed model is validated against a diverse set of analytical and experimental benchmarks, each varying in complexity. Lastly, we investigate the impact of wettability on the evaporation dynamics of a liquid droplet on a solid substrate.