A search is performed in the invariant mass spectrum of the B c + π+π− system for the excited B c + states B c (21S0)+ and B c (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 B c (21S0)+ and B c (23S1)+ states times the branching fractions of B c (21S0)+ → B c + π+π− and B c (23S1)+ → B c * +π+π− over the production cross-section of the B c + 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 B c (21S0)+ and B c (23S1)+ in the mass ranges [6830, 6890] MeV/c2 and [6795, 6890] MeV/c2, respectively.