Honeycomb magnets with strong spin-orbit coupling (SOC) are expect to produce exotic magnetic ground states as exemplified by d5 iridates with Jeff = 1/2 state. In d4 case, SOC produces Jeff = 0 states which may interact magnetically via excited Jeff = 1 states. Unconventional magnetic ground states, like spin-liquids, are predicted when the Jeff = 0 states are placed on a honeycomb lattice. We focused on honeycomb ruthenate Na2RuO3 as a possible Jeff = 0 system. In contrast to the previous report, our Na2RuO3 sample, prepared with special care about air-sensitivity, did not show magnetic order down to 2 K, and spin-liquid-like behaviour was seen. There are several scenarios for the nonmagnetic behaviour, such as Jeff = 0 singlet or J1-J2 frustration. In order to reveal the origin of nonmagnetic state, we propose to perform inelastic neutron scattering experiments at MARI and LET.