Hepatocellular carcinoma (HCC) is a complex disease involving altered interactomes of transcripts and proteins. MicroRNAs (miRNAs) are small-noncoding RNAs that can interact with specific gene transcripts and an array of other vital endogenous non-coding RNAs (lncRNAs) that can influence gene expression. Maternally Expressed Gene 3 (MEG3) is an imprinted lncRNA that is reported to be downregulated in HCC (in both cell lines and tumors). Alcohol Dehydrogenase 4 (ADH4) is a well-known prognostic protein biomarker for predicting the survival outcomes of patients with hepatocellular carcinoma whose expression is regulated by miR-664a-3p, which is upregulated in HCC. In this study, we performed a battery of robust and systematic in silico analyses to predicate the possible lncRNA-miRNA interactions between MEG3, miR-664a-3p, and ADH4. miRNA-mRNA and lncRNA-miRNA hybrid structures were primarily obtained, and the minimum free energies (MFEs) for the 3'UTR (Untranslated Regions) of ADH4-miR-664a-3p and the 3'UTR of MEG3-miR-664a-3p interactions were assessed to predict the stability of the obtained RNA heteroduplex hybrids. The hybrid with the least minimum free energy (MFE) was considered to be the most favorable. The MFEs were around -28.1 kcal/mol and -31.3 kCal/mol for the ADH4-miR-664a-3p and MEG3-miR-66a-3p RNA hybrids, respectively. This demonstrated that lncRNA-MEG3 might be a competitive endogenous RNA that acts as a molecular sponge for miR-664a-3p. In summary, our interaction analyses results predict the significance of the MEG3/miR-664a-3p/ADH4 axis, where MEG3 downregulation results in miR-664a-3p overexpression and the subsequential underexpression of ADH4 in HCC, as a novel axis of interest that demands further validation.