We investigate the potential of using massive clusters as gravitational telescopes for searches and studies of supernovae of Type Ia and Type II in optical and near-infrared bands at central wavelengths in the interval 0.8-1.25 \mu m. Using high-redshift supernova rates derived from the measured star formation rate , we find the most interesting effects for the detection of core-collapse SNe in searches at limiting magnitudes m _ { lim } \sim 25 - 26.5 mag , where the total detection rate could be significantly enhanced and the number of detectable events is considerable even in a small field . For shallower searches , \sim 24 , a net gain factor of up to 3 in the discovery rate could be obtained , and yet a much larger factor for very high source redshifts . For programs such as the GOODS/ACS transient survey , the discovery rate of supernovae beyond z \sim 2 could be significantly increased if the observations were done in the direction of massive clusters . For extremely deep observations , m _ { lim } > 27 mag , or for very bright SNe ( e.g . Type Ia ) the competing effect of field reduction by lensing dominates , and fewer supernovae are likely to be discovered behind foreground clusters .