The upcoming Ooty Wide Field Array (OWFA) will operate at $326.5 \, {\rm MHz}$ which corresponds to the redshifted 21-cm signal from neutral hydrogen (HI) at z = 3.35. We present two different prescriptions to simulate this signal and calculate the visibilities expected in radio-interferometric observations with OWFA. In the first method we use an input model for the expected 21-cm power spectrum to directly simulate different random realizations of the brightness temperature fluctuations and calculate the visibilities. This method, which models the HI signal entirely as a diffuse radiation, is completely oblivious to the discrete nature of the astrophysical sources which host the HI. While each discrete source subtends an angle that is much smaller than the angular resolution of OWFA, the velocity structure of the HI inside the individual sources is well within the reach of OWFA’s frequency resolution and this is expected to have an impact on the observed HI signal. The second prescription is based on cosmological N-body simulations. Here we identify each simulation particle with a source that hosts the HI, and we have the freedom to implement any desired line profile for the HI emission from the individual sources. Implementing a simple model for the line profile, we have generated several random realizations of the complex visibilities. Correlations between the visibilities measured at different baselines and channels provides an unique method to quantify the statistical properties of the HI signal. We have used this to quantify the results of our simulations, and explore the relation between the expected visibility correlations and the underlying HI power spectrum.