This article presents a novel hybrid approach for electromagnetic near-field scanning, combining model-based, i.e., Gaussian processes regression, and data-driven, i.e., dynamic mode decomposition, techniques. We first leverage the Latin hypercube sampling technique to achieve spatially sparse measurements. Subsequently, dynamic mode decomposition is applied to analyze the resulting spatiotemporal data with sparse spatial sampling, enabling the extraction of both frequency information and sparse dynamic modes. Finally, the Gaussian processes regression, also known as the Kriging method, is adopted for the full-state reconstruction. The proposed hybrid approach is benchmarked by an example of the crossed dipole antennas. The obtained results demonstrate that with a sparse spatial sampling factor of 130, the proposed approach can achieve a complete reconstructed field distribution suitable for engineering applications, along with accurate extraction of frequency information. Consequently, our hybrid framework offers a promising avenue for augmenting the efficiency and accuracy of electromagnetic near-field scanning, with the potential for application in diverse electromagnetic measurement scenarios.