Theoretical studies suggest that a giant planet around the young star MWC 758 could be responsible for driving the spiral features in its circumstellar disk. Here, we present a deep imaging campaign with the Large Binocular Telescope with the primary goal of imaging the predicted planet. We present images of the disk in two epochs in the $L^{prime}$ filter (3.8 $mu m$) and a third epoch in the $M^{prime}$ filter (4.8 $mu m$). The two prominent spiral arms are detected in each observation, which constitute the first images of the disk at $M^prime$, and the deepest yet in $L^prime$ ($Delta L^prime=$12.1 exterior to the disk at 5$sigma$ significance). We report the detection of a S/N$sim$3.9 source near the end of the Sourthern arm, and, from the sources detection at a consistent position and brightness during multiple epochs, we establish a $sim$90% confidence-level that the source is of astrophysical origin. We discuss the possibilities that this feature may be a) an unresolved disk feature, and b) a giant planet responsible for the spiral arms, with several arguments pointing in favor of the latter scenario. We present additional detection limits on companions exterior to the spiral arms, which suggest that a $lesssim$4 M$_{Jup}$ planet exterior to the spiral arms could have escaped detection. Finally, we do not detect the companion candidate interior to the spiral arms reported recently by Reggiani et al. (2018), although forward modelling suggests that such a source would have likely been detected.
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