The leaf area index (LAI) is a key biophysical variable for agroecosystem monitoring, as well as a relevant state variable in crop modelling. For this reason, temporal and spatial determination of LAI are required to improve the understanding of several land surface processes related to vegetation dynamics and crop growth. Despite the large number of retrieved LAI products and the efforts to develop new and updated algorithms for LAI estimation, the available products are not yet capable of capturing site-specific variability, as requested in many agricultural applications. The objective of this study was to evaluate the potential of non-parametric approaches for multi-temporal LAI retrieval by Sentinel-2 multispectral data, in comparison with a VI-based parametric approach. For this purpose, we built a large database combining a multispectral satellite data set and ground LAI measurements collected over two growing seasons (2018 and 2019), including three crops (i.e., winter wheat, maize, and alfalfa) characterized by different growing cycles and canopy structures, and considering different agronomic conditions (i.e., at three farms in three different sites). The accuracy of parametric and non-parametric methods for LAI estimation was assessed by cross-validation (CV) at both the pixel and field levels over mixed-crop (MC) and crop-specific (CS) data sets. Overall, the non-parametric approach showed a higher accuracy of prediction at pixel level than parametric methods, and it was also observed that Gaussian Process Regression (GPR) did not provide any significant difference (p-value > 0.05) between the predicted values of LAI in the MC and CS data sets, regardless of the crop. Indeed, GPR at the field level showed a cross-validated coefficient of determination (R2CV) higher than 0.80 for all three crops.