The origin of a mysterious pseudogap region in high-Tc superconductors is a challenging issue. It was proposed that the pseudogap is caused by a circulating-current order characterized by a unique long-range patten of loop currents in the CuO2 planes. Loop-current order is by now inferred in 5 different classes of symmetry-sensitive experiments: polarized neutron scattering, Kerr effect, bireferingence, dichroic ARPES, and second harmonic generation. However, local probes such as MuSR and NMR do not see the magnetic fields expected for such an order. These local probes have much longer time scales than the others. It has been suggested that the local magnetic fields may be motionally narrowed by fluctuations among the different possible directions of the loop-current order. We propose MuSR experiments to fairly definitively this possibility and also obtain the fluctuation time-scale.