In this paper, we consider the problem of estimating the target sound direction of arrival (DoA) for a hearing aid (HA) system, which can connect to a wireless microphone worn by the talker of interest. The wireless microphone “informs” the HA system about the noise-free target speech. To estimate the DoA, we consider a maximum-likelihood approach, and we assume that a database of DoA-dependent relative transfer functions (RTFs) has been measured in advance and is available. The proposed DoA estimator is able to take the available noise-free target speech, ambient noise characteristics, and the shadowing effect of the user's head on the received signals into account, and it supports both monaural and binaural microphone array configurations. Moreover, we analytically analyze the bias in the proposed estimator and introduce a modified estimator, which has been compensated for the bias. We demonstrate that the proposed method has lower computational complexity and better performance than recent RTF-based estimators. Furthermore, to decrease the number of parameters required to be wirelessly exchanged between the HAs in binaural configurations, we propose an information fusion strategy, which avoids transmitting microphone signals between the HAs. An important benefit of the proposed IF strategy is that the number of parameters to be exchanged between the HAs is independent of the number of HA microphones. Finally, we investigate the performance of variants of the proposed estimator extensively in different noisy and reverberant situations.