During the cell cycle, the organization of the cytoskeletal network undergoes dramatic changes. In order to reveal possible changes of the viscoelastic properties in the intracellular space during the cell cycle we investigated the diffusion of endogenous lipid granules within the fission yeast Schizosaccharomyces Pombe using optical tweezers. The cell cycle was divided into interphase and mitotic cell division, and the mitotic cell division was further subdivided in its stages. During all stages of the cell cycle, the granules predominantly underwent subdiffusive motion, characterized by an exponent alpha that is also linked to the viscoelastic moduli of the cytoplasm. The exponent alpha was significantly smaller during interphase than during any stage of the mitotic cell division, signifying that the cytoplasm was more elastic during interphase than during division. We found no significant differences in the subdiffusive exponents from granules measured in different stages of cell division. Also, our results for the exponent displayed no significant dependence on the position of the granule within the cell. The observation that the cytoplasm is more elastic during interphase than during mitotic cell division is consistent with the fact that elastic cytoskeletal elements such as microtubules are less abundantly present during cell division than during interphase.