This contribution addressees the problem of the theoretical assessment of the bit rate reduction that can be achieved through foveated image compression for codecs operating in the DCT domain. Modeling the image components as Compound Gaussian Random Fields (CGRFs), we extend the mathematical analysis of the DCT coefficient distributions reported in [1] to foveated images. As a general result, we demonstrate that the DCT coefficients of low pass filtered image blocks can be effectively modelled with Laplacian distributions. This property allows us to express the Shannon rate reduction achievable with foveated compression in a simple and compact form as function of the foveal filter coefficients. Experiments results used to validate the theoretical analysis are also included.