A search is performed in the invariant mass spectrum of the Bc +π+π− system for the excited Bc + states Bc(21S0)+ and Bc(23S1)+ using a data sample of pp collisions collected by the LHCb experiment at the centre-of-mass energy of s=8 TeV, corresponding to an integrated luminosity of 2 fb−1. No evidence is seen for either state. Upper limits on the ratios of the production cross-sections of the Bc(21S0)+ and Bc(23S1)+ states times the branching fractions of Bc(21S0)+ → Bc +π+π− and Bc(23S1)+ → Bc * +π+π− over the production cross-section of the Bc + state are given as a function of their masses. They are found to be between 0.02 and 0.14 at 95% confidence level for Bc(21S0)+ and Bc(23S1)+ in the mass ranges [6830, 6890] MeV/c2 and [6795, 6890] MeV/c2, respectively.[Figure not available: see fulltext.].