The observation potential of the decays B0s,d → J/ψη with the ATLAS detector at the LHC is described in this paper. At present there exist only upper limits for the branching fractions, but at LHC, a clear signal for the decay mode B0s,d → J/ψη is expected. The branching fraction of this decay mode can thus be measured, and other parameters such as B0s lifetime can be measured as well. The decay mode B0s → J/ψη is analogous to the mode B0s → J/ψφ, which has been studied extensively in view of CP violation measurements. In these two decay modes, the CP asymmetry predicted by the Standard Model is very small, and the observation of a sizeable effect would be a signal of physics beyond the Standard Model. The decay mode J/ψη constitutes thus a cross-check for the mode J/ψφ. Furthermore, the former final state is a CP-eigenstate and no angular analysis is thus needed. The reconstruction of η-mesons at LHC experiments has not been addressed before, and therefore the study presented here can also be regarded as an example of the physics prospects with η-mesons at the LHC.