The Time Difference of Arrival (TDOA) of an acoustic source with respect to a given pair of microphones is typically estimated as the maximizer of a Measure of Synchrony (MoS) between the pair of microphone signals, within the interval [-D/v, D/v], where D is the inter-microphone distance and v is the speed of sound. In practical enclosures, phantom sources are created due to reverberation, which can cause false peaks in the MoS, leading to erroneous TDOA estimates. In several practical enclosures such as meeting rooms, conference halls, lecture halls, etc., the regions which can admit an acoustic source are restricted, because of furniture and other fixtures. Consequently, it is possible to acquire prior knowledge of the region which can accommodate an acoustic source. In this paper, we propose an approach to utilize this prior knowledge of source region for accurate TDOA estimation. We transform the prior knowledge of source region into an interval of possible TDOAs using a newly developed concept of family of hyperboloids. This interval, referred to as Region Constrained TDOA Interval (RCTI) is shown to be smaller than [-D/v, D/v]. TDOA is then estimated as the maximizer of a suitable MoS within the RCTI. We demonstrate that estimating TDOA within RCTI, with generalized cross correlation (GCC) class of functions as MoS, is more robust to reverberation than estimating TDOA within [-D/v, D/v].