Accurate prediction of jet noise remains a major challenge in computational aeroacoustics due to the high computational cost associated with resolving both the jet near- and far-field. In the present work, we perform large-eddy simulations (LES) for isothermal compressible round jets at high Reynolds number at the inflow, using high-order compact finite difference schemes. The acoustic propagation in the far-field is calculated by solving isentropically linearized Euler equations (ILEE) using the same high-order compact finite difference schemes as the near-field LES. Unlike the conventional one-way coupling approach, in which near-field flow information is passed to the far-field solver without feedback, in the present two-way coupling approach, far-field results are taken into account when calculating near-field variables. Results show smooth acoustic wave propagation across the coupling interface. The predicted potential core lengths, jet spreading rates, and axial variation of overall sound pressure level are consistent with trends reported in earlier experimental and numerical studies. The results demonstrate that two-way coupling is a robust and physically consistent approach for direct jet noise computation for compressible round jets.