Synthetic aperture radar (SAR) images have found numerous applications. However, analysis of SAR images including interpretation, classification, segmentation, etc. is an extremely challenging task due to the presence of intensive speckle noise. Therefore, image denoising is one of the main stages in SAR data pre-processing. Over the past decades, a large number of different image denoising techniques have been proposed ranging from local statistics filters to deep learning based ones. In this study, we analyze one of the most known and widely used local statistics Frost filter. Despeckling efficiency of the Frost filter significantly depends on the sliding window size and tuning (also called damping) factor. Here, we present a method for optimal parameters selection of the Frost filter for a given image based on despeckling efficiency prediction. Despeckling efficiency prediction is carried out using a set of statistical and spectral input parameters and a multilayer neural network. It is shown that such a prediction can be performed before applying image despeckling with a high accuracy and it is faster than despeckling itself. Both simulated speckled images and real-life Sentinel-1 SAR images have been used for extensive evaluation of the proposed method.