In this study, a low probability of intercept (LPI)-based orthogonal frequency division multiplexing radar waveform design strategy is developed for target time delay estimation in a cooperative radar-communications system, where the communications base station (CBS) is able to receive and process the radar emissions. The basis of the LPI-based radar waveform design strategy is to utilise the optimisation technique to design the transmitted waveform of a radar system for specified target time delay estimation accuracy in order to achieve enhanced LPI performance. The expression for Cramer–Rao lower bound is analytically derived and utilised as a performance metric for target time delay estimation performance. The resulting optimisation problem is solved by the approach of linear programming. Several numerical results are provided to verify the superiority of the proposed radar waveform design algorithm in terms of the LPI performance of the radar system. It is also shown that the radar transmitted power can be significantly reduced with the help from the CBS which plays a role of the bistatic radar receiver.