Nanoviscosity of the cytoplasm is a key factor affecting diffusion of biomolecules and - as a consequence - rates of biochemical reactions in a cell. Nanoviscosity is an outcome of variable chemical and structural factors, which can temporarily change with cell-cycle associated changes of intracellular architecture. Thus, the question arises, whether rates of biochemical reactions depend on the point of cell cycle. In this paper we address this topic by constant observation of nanoviscosity of HeLa cells cytoplasm during S, G2 and G1 phases after Aphidicolin synchronization. For this purpose we measured diffusion rates of EGFP molecules using fluorescence correlation spectroscopy (FCS). To our surprise, a counter-intuitive stability of cytoplasmic viscosity was observed during the cell cycle. Our results hint at possible existence of robust mechanism maintaining stable physiological viscosity of the cytoplasm, despite huge structural changes during cell cycle.