In conventional superconductors, very narrow superconducting-fluctuation regions are observed above Tc, because strong overlap of Cooper pairs occurs in a coherence volume 4 π ξ3/3 with ξ being the coherence length. In the bulk form of iron-chalcogenide superconductor FeSe, it is argued that the system may be located in the crossover region from Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC), where strong superconducting fluctuations are expected. In this respect, we carried out magnetization, specific heat, and Nernst effect measurements on FeSe single crystals in order to investigate the superconducting fluctuation effect near Tc. The temperature range of diamagnetization induced by superconducting fluctuations seems very narrow above Tc. The temperature-dependent magnetization curves measured at different magnetic fields do not cross at a single point. This is in sharp contrast to the situation in many cuprate superconductors, where such a crossing point has been taken as a clear signature of strong critical fluctuations. The magnetization data can be scaled according to the Ginzburg-Landau fluctuation theory for a quasi-two-dimensional system. However the scaling result cannot be described by the theoretical function of the fluctuation theory due to the limited fluctuation regions. The specific heat jump near Tc is rather sharp without the trace of strong superconducting fluctuations. This is also supported by the Nernst effect measurements which indicate a very narrow region for vortex motion above Tc. Associated with a very small value of Ginzburg number and further analyses, we conclude that the superconducting fluctuations are vanishingly weak above Tc in this material. Our results are strongly against the picture of significant phase fluctuations in FeSe single crystals, although the system has a very limited overlap of Cooper pairs in the coherence volume. This dichotomy provides new insights into the superconducting mechanism when the system is with a dilute superfluid density.