We studied the dissolution of microcrystalline cellulose (MCC) in mixtures of dimethyl sulfoxide (DMSO) with 32 ionic liquids (ILs), at a fixed temperature (70 °C) and mole fraction of DMSO (χDMSO = 0.6). Under these conditions, employing a recommended dissolution protocol, MCC dissolved in 19 IL-DMSO mixtures. In order to access quantitatively the relative importance (to biopolymer dissolution) of cellulose-solvent interactions, we correlated the mass fraction of dissolved cellulose (MCC-m%) with physicochemical properties of these mixtures. The solvent descriptors that gave the best correlations are Lewis acidity and Lewis basicity (calculated from the UV–Vis spectra of solvatochromic probes), the molar volume of the IL, and the Lorentz-Lorenz refractive index function of the IL-DMSO mixtures. This result is similar to that observed when solvent empirical polarities of these binary mixtures were correlated with the same descriptors. The multi-parameter correlations quantify, for the first time, the relative importance of cellulose-solvent interactions. Our results agree with the established opinion that an efficient cellulose solvent should disrupt the inter- and intramolecular hydrogen bonding in cellulose, and the hydrophobic interactions present due to the amphiphilic nature of the biopolymer.