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Microseismic source localization is vital for applications like C02 injection monitoring, geothermal project evaluation, and earthquake detection. Traditional localization methods, such as those based on traveltimes and wavefields, require dense seismic networks, and are costly. To address these limitations, we propose a novel Fourier Neural Operator (FNO)-based method, we refer to as source-embedding FNO (SFNO). SFNO integrates source coordinates into its architecture and utilizes physics-informed loss functions to refine source locations in the inversion stage iteratively. Numerical experiments using a realistic velocity model demonstrate that this approach achieves accurate and efficient source localization without requiring precise velocity models. The methodology shows that the neural operator-based method is efficient in real-time microseismic monitoring and can be further used in field data.