Extremely large aperture arrays (ELAAs) can offer massive spatial multiplexing gains in the radiative near-field region in beyond 5G systems. While near-field channel modeling for uniform linear arrays has been extensively explored in the literature, uniform planar arrays - despite their advantageous form factor - have been somewhat neglected due to their more complex nature. Spatial correlation is crucial for non-line-of-sight channel modeling. Unlike far-field scenarios, the spatial correlation properties of near-field channels have not been thoroughly investigated. In this paper, we start from the fundamentals and develop a near-field spatial correlation model for arbitrary spatial scattering functions. Furthermore, we derive the lower-dimensional subspace where the channel vectors can exist. It is based on prior knowledge of the three-dimensional coverage region where scattering clusters exists and we derive a tractable one-dimensional integral expression. This subspace is subsequently employed in the reduced-subspace least squares (RSLS) estimation method for near-field channels, thereby enhancing performance over the traditional least squares estimator without the need for having full spatial correlation matrix knowledge.