Context. The high star formation rates of luminous infrared galaxies (LIRGs) make them ideal places for core-collapse supernova (CCSN) searches. Massive star formation can often be found in coexistence with an active galactic nucleus (AGN), contributing jointly to the energy source of LIRGs. At radio frequencies, where light is unaffected by dust extinction, it is possible to detect compact components within the innermost LIRG nuclear regions, such as SNe and SN remnants, as well as AGN buried deep in the LIRG nuclei. Aims. Our study of the LIRG IC 883 aims at: (i) investigating the parsec-scale radio structure of the (circum-)nuclear regions of IC 883; (ii) detecting at radio frequencies the two recently reported circumnuclear SNe 2010cu and 2011hi, which were discovered by near-IR (NIR) adaptive optics observations of IC 883; and (iii) further investigating the nature of SN 2011hi at NIR wavelengths. Methods. We used the electronic European very long baseline interferometry (VLBI) Network (e-EVN) at 5 GHz, and the electronic Multi-Element Remotely Linked Interferometer Network (e-MERLIN) at 6.9 GHz, to observe contemporaneously the LIRG IC 883 at high angular-resolution (from tens to hundreds of milliarcsec) and with high sensitivity (<70 μJy), complemented by archival VLBI data at 5 GHz and 8.4 GHz. We also used the Gemini North telescope to obtain late-time JHK photometry for SN 2011hi. Results. The circumnuclear regions traced by e-MERLIN at 6.9 GHz have an extension of ∼1 kpc, at a position angle of 130 • , and show a striking double-sided structure, which very likely corresponds to a warped rotating ring, in agreement with previous studies. Our e-EVN observations at 5 GHz and complementary archival VLBI data at 5 GHz and 8.4 GHz, reveal various milliarcsec compact components in the nucleus of IC 883. A single compact source, an AGN candidate, dominates the emission at both nuclear and circumnuclear scales, as imaged with the e-EVN and e-MERLIN, respectively. The other milliarcsec components are strongly indicative of ongoing nuclear CCSN activity. Our e-EVN observations also provided upper limits to the radio luminosity of the two SNe in IC 883 recently discovered at NIR wavelengths. We refine the classification of SN 2011hi as a Type IIP SN according to our latest epoch of Gemini North observations acquired in 2012, in agreement with a low-luminosity radio SN nature. We estimate a CCSN rate lower limit of 1.1 +1.3 −0.6 yr −1 for the entire galaxy, based on three nuclear radio SNe and the circumnuclear SNe 2010cu and 2011hi.