Using Focus of Attention (FoA) as a perceptual process in image and video compression belongs to well-known approaches to increase coding efficiency. It has been shown that foveated coding, when compression quality varies across the image according to region of interest, is more efficient than the alternative coding, when all region are compressed in a similar way. However, widespread use of such foveated compression has been prevented due to two main conflicting causes, namely, the complexity and the efficiency of algorithms for FoA detection. One way around these is to use as much information as possible from the scene. Since most video sequences have an associated audio, and moreover, in many cases there is a correlation between the audio and the visual content, audiovisual FoA can improve efficiency of the detection algorithm while remaining of low complexity. This paper discusses a simple yet efficient audiovisual FoA algorithm based on correlation of dynamics between audio and video signal components. Results of audiovisual FoA detection algorithm are subsequently taken into account for foveated coding and compression. This approach is implemented into H.265/HEVC encoder producing a bitstream which is fully compliant to any H.265/HEVC decoder. The influence of audiovisual FoA in the perceived quality of high and ultra-high definition audiovisual sequences is explored and the amount of gain in compression efficiency is analyzed.