This paper presents a different approach to tackle the Sound Source Localization (SSL) problem apply on a compact microphone array that can be mounted on top of a small moving robot in an indoor environment. Sound source localization approaches can be categorized into the three main categories; Time Difference of Arrival (TDOA), high-resolution subspace-based methods, and steered beamformer-based methods. Each method has its limitations according to the search or application requirements. Steered beamformer-based method will be used in this paper because it has proven to be robust to ambient noise and reverberation to a certain extent. The most successful and used algorithm of this method is the SRP-PHAT algorithm. The main limitation of SRP-PHAT algorithm is the computational burden resulting from the search process, this limitation comes from searching among all possible candidate locations in the searching space for the location that maximizes a certain function. The aim of this paper is to develop a computationally viable approach to find the coordinate location of a sound source with acceptable accuracy. The proposed approach comprises two stages: the first stage contracts the search space by estimating the Direction of Arrival (DoA) vector from the time difference of arrival with an addition of reasonable error coefficient around the vector to make sure that the sound source locates inside the estimated region, the second stage is to apply the SRP-PHAT algorithm to search only in this contracted region for the source location. The AV16.3 corpus was used to evaluate the proposed approach, extensive experiments have been carried out to verify the reliability of the approach. The results showed that the proposed approach was successful in obtaining good results compared to the conventional SRP-PHAT algorithm.