The acetylation modification process of histone has an essential role in the epigenetic regulation of gene expression. This process is controlled by the balance between histone deacetylases (HDAC) and histone acetyltransferases (HAT). HDACs are thought to be vital for cell function. Particularly, higher HDAC expression is frequent in various cancers, resulting in the dysregulation of several target genes involved in cell proliferation, differentiation, and survival. In this study, the inhibitory feasibility of several HDAC inhibitors was investigated, including vorinostat (SAHA), N-hydroxy-3-phenylprop-2-enamide (CPD1), N-hydroxy-3-(pyridine-4-yl)prop-2-enamide (CPD2), N-hydroxy-3-(pyridine-2-yl)prop-2-enamide (CPD3), 4-(diphenylamino)-N-(5-(hydroxyamino)-5-oxopentyl)benzamide (CPD4), 2-(6-(((6-fluoronaphthalen-2-yl)methyl)amino)-3-azabicyclo[3.1.0]hex-3-yl)-N-hydroxypirimidine-5-carboxamide (CPD5), and N-(3-aminopropyl)-N-hydroxy-2-((naphthalene-1-yloxy)methyl)oct-2-enediamide (CPD6). By examining the stability of the enzyme, positional stability of the individual amino acids, and binding energies of HDLP-inhibitor complexes, the inhibitory feasibility was assessed. The complexes of the HDLP enzyme with SAHA, CPD4, CPD5, and CPD6 had higher stability than the other studied complexes, according to the results of trajectory analysis and the Ramachandran plot. Based on the calculated MM-PBSA binding free energies, the stability of the HDLP enzyme followed this order CPD4 > CPD5 > SAHA > CPD6 > CPD2 > CPD3 > CPD1. The drugability values followed the same trend as the previous ones. Based on the obtained in silico results, CPD4, CPD5, and CPD6 were discovered to be possible lead compounds as reference inhibitors of SAHA.