Our knowledge on the active three-neutrino mixing angles (θ 12 , θ 13 , and θ 23 ) and the Dirac CP phase δ CP is becoming accurate day-by-day enabling us to test the unitarity of the leptonic mixing matrix with utmost precision. Future high-precision longbaseline experiments are going to play an important role in this direction. In this work, we study the impact of possible non-unitary neutrino mixing (NUNM) in the context of nextgeneration long-baseline experiments DUNE and T2HKK/JD+KD having one detector in Japan (T2HK/JD) and a second detector in Korea (KD). We estimate the sensitivities of these setups to place direct, model-independent, and competitive constraints on various NUNM parameters. We demonstrate the possible correlations between the NUNM parameters and the oscillations parameters θ 23 and δ CP . Our numerical results, supported by simple approximate analytical expressions of the oscillation probabilities in matter, reveal that JD+KD has better sensitivities for |α 21 | and α 22 as compared to DUNE, due to its larger statistics in the appearance channel and less systematic uncertainties in the disappearance channel, respectively. For |α 31 |, |α 32 |, and α 33 , DUNE gives better constraints as compared to JD+KD, due to its larger matter effect and wider neutrino energy spectrum. For α 11 , both DUNE and JD+KD give similar bounds. We also show how much the bounds on the NUNM parameters can be improved by combining the prospective data from DUNE and JD+KD setups. Due to the presence of zero-distance effects, the data from near detectors in both DUNE and JD+KD experiments, can further improve the limits on |α 21 | considerably, while giving slightly better constraints for α 11 and α 22 . Finally, we observe that the ν τ appearance sample in DUNE can improve the constraints on |α 32 | and α 33 .