Using hourly atmospheric surface pressure field from ECMWF (European Centre for Medium-Range Weather Forecasts) and from NCEP (National Centers for Environmental Prediction) Climate Forecast System Reanalysis (CFSR) models, we show that atmospheric pressure fluctuations excite the translational oscillation of the inner core, the so-called Slichter mode, to the sub-nanogal level at the Earth surface. The computation is performed using a normal-mode formalism for a spherical, self-gravitating anelastic PREM-like Earth model. We determine the statistical response in the form of power spectral densities of the degree-one spherical harmonic components of the observed pressure field. Both hypotheses of inverted and non-inverted barometer for the ocean response to pressure forcing are considered. Based on previously computed noise levels, we show that the surface excitation amplitude is below the limit of detection of the superconducting gravimeters, making the Slichter mode detection a challenging instrumental task for the near future.