The transverse target spin azimuthal asymmetry AUTsin(ϕ−ϕS) in hard exclusive production of ρ0 mesons was measured at COMPASS by scattering 160 GeV/c muons off transversely polarised protons and deuterons. The measured asymmetry is sensitive to the nucleon helicity-flip generalised parton distributions Eq, which are related to the orbital angular momentum of quarks in the nucleon. The Q2, xBj and pT2 dependence of AUTsin(ϕ−ϕS) is presented in a wide kinematic range: 1(GeV/c)2<Q2<10(GeV/c)2, 0.003<xBj<0.3 and 0.05(GeV/c)2<pT2<0.5(GeV/c)2 for protons or 0.10(GeV/c)2<pT2<0.5(GeV/c)2 for deuterons. Results for deuterons are obtained for the first time. The measured asymmetry is small in the whole kinematic range for both protons and deuterons, which is consistent with the theoretical interpretation that contributions from GPDs Eu and Ed approximately cancel.