Fluid‐induced stress perturbations in the crust at seismogenic depths caused by sources such as tidal or seasonal loading may trigger earthquakes. We investigate the role of small periodic pore pressure (Pp) perturbation in rupture nucleation by performing laboratory triaxial creep experiments on Fontainebleau sandstone, saturated in water, under sinusoidal Pp variations. Results show that recorded acoustic emissions (AEs) correlate with Pp as the rock approaches failure. More interestingly, AEs occur significantly more when Pp is decreasing, that is, when strain rate is maximum with a progressive increase of Pp‐AEs correlation in time as the rock approaches failure. This suggests that the correlation of small stress perturbations and AEs not only depends on Pp amplitude but also on the criticality of the rock. Observations at the laboratory scale support field observations where tidal loading may have modulated seismic rates during the nucleation phase of the 2004 Sumatra‐Andaman and 2011 Tohoku‐Oki earthquakes.