The detection of obscured supernovae (SNe) in near-infrared monitoring campaigns of starburst galaxies has shown that a significant fraction of SNe is missed by optical surveys. However, the number of SNe detected in ground-based near-IR observations is still significantly lower than the number of SNe extrapolated from the FIR luminosity of the hosts. A possibility is that most SNe occur within the nuclear regions, where the limited angular resolution of ground-based observations prevents their detection. This issue prompted us to exploit the superior angular resolution of NICMOS-HST to search for obscured SNe within the first kpc from the nucleus of strong starbursting galaxies. A total of 17 galaxies were observed in SNAPSHOT mode. Based on their FIR luminosity, we expected to detect not less than ~12 SNe. However, no confirmed SN event was found. From our data we derive an observed nuclear SN rate <0.5 SN/yr per galaxy. The shortage of SN detections can be explained by a combination of several effects. The most important are: i) the existence of a strong extinction, A_V>11; ii) most SNe occur within the first 0.5" (which corresponds in our sample to about 500pc) where even NICMOS is unable to detect SN events. Comment: 7 pages, accepted for publication in A&A