This article treats the problem of time delay estimation in a multirate asynchronous direct-sequence code-division multiple access (DS-CDMA) system in a near-far scenario. A subspace based algorithm for the time delayestimation problem is proposed. The algorithm is a minor modified version of the MUSIC estimator proposed by Ostman, Parkvall and Ottersten (see Proceedings of the 31st Asilomar Conference on Signals, Systems and Computers, 1997). Through theoretical analysis and simulations it is shown that the subspace approach to timedelay estimation in a multirate DS-CDMA system is applicable when the algorithm is applied in a way such that the low-rank structure of the system is conserved.