A search for the narrow structure, X ( 5568 ) , reported by the D0 Collaboration in the decay sequence X → B 0 s π ± , B 0 s → J / ψ ϕ , is presented. The analysis is based on a data sample recorded with the ATLAS detector at the LHC corresponding to 4.9 fb − 1 of p p collisions at 7 TeV and 19.5 fb − 1 at 8 TeV. No significant signal was found. Upper limits on the number of signal events, with properties corresponding to those reported by D0, and on the X production rate relative to B 0 s mesons, ρ X , were determined at 95% confidence level. The results are N ( X ) < 382 and ρ X < 0.015 for B 0 s mesons with transverse momenta above 10 GeV, and N ( X ) < 356 and ρ X < 0.016 for transverse momenta above 15 GeV. Limits are also set for potential B 0 s π ± resonances in the mass range 5550 to 5700 MeV.