Novel coronavirus disease 2019 (COVID-19) emerges as a serious threat to public health globally. The rapid spreading of COVID-19, caused by severe acute respiratory syndrome (SARS) coronavirus 2 (SARS-CoV-2), proclaimed the multitude of applied research needed not only to save the human health but also for the environmental safety. As per the recent World Health Organization reports, the novel corona virus may never be wiped out completely from the world. In this connection, the inhibitors already designed against different targets of previous human coronavirus (HCoV) infections will be a great starting point for further optimization. Pinpointing biochemical events censorious to the HCoV lifecycle has provided two proteases: a papain-like protease (PLpro) and a 3C-like protease (3CLpro) enzyme essential for viral replication. In this study, naphthyl derivatives inhibiting PLpro enzyme were subjected to robust molecular modelling approaches to understand different structural fingerprints important for the inhibition. Here, we cover two main aspects such as (a) exploration of naphthyl derivatives by classification QSAR analyses to find important fingerprints that module the SARS-CoV PLpro inhibition and (b) implications of naphthyl derivatives against SARS-CoV-2 PLpro enzyme through detailed ligand–receptor interaction analysis. The modelling insights will help in the speedy design of potent broad spectrum PLpro inhibitors against infectious SARS-CoV and SARS-CoV-2 in the future.Graphical Supplementary InformationThe online version contains supplementary material available at(10.1007/s11030-021-10198-3) .