Using Non-Redundant Mask interferometry (NRM), we searched for binary companions to objects previously classified as transitional discs (TD). These objects are thought to be an evolutionary stage between an optically thick disc and optically thin disc. We investigate the presence of a stellar companion as a possible mechanism of material depletion in the inner region of these discs, which would rule out an ongoing planetary formation process in distances comparable to the binary separation. For our detection limits, we implement a new method of completeness correction using a combination of randomly sampled binary orbits and Bayesian inference. The selected sample of 24 TDs belongs to the nearby and young star-forming regions: Ophiuchus (similar to 130 pc), Taurus-Auriga (similar to 140 pc) and IC348 (similar to 220 pc). These regions are suitable to resolve faint stellar companions with moderate to high confidence levels at distances as low as 2 au from the central star. With a total of 31 objects, including 11 known TDs and circumbinary discs from the literature, we have found that a fraction of 0.38 +/- 0.09 of the SEDs of these objects are likely due to the tidal interaction between a close binary and its disc, while the remaining SEDs are likely the result of other internal processes such as photoevaporation, grain growth, planet-disc interactions. In addition, we detected four companions orbiting outside the area of the truncation radii and propose that the IR excesses of these systems are due to a disc orbiting a secondary companion.