This paper represents a first attempt of embedding the Barycentric Celestial Reference System, the fundamental relativistic reference system to be used for the modelling of Gaia observations, into some cosmological background. The general Robertson-Walker metric is transformed into local coordinates where the cosmological effects are represented as tidal potentials. A version of a cosmological BCRS is then suggested to lowest order. The effects of cosmological background on the motion of the Solar System are estimated and found to be completely negligible. The relation to the de Sitter and Schwarzschild-de Sitter solutions is discussed.