Recently, ionic liquids have been studied as promising solvents for cellulose. Since ionic liquids can be combined freely from different cations and anions, possible candidates are numerous. Therefore, a time efficient method to screen ionic liquids with respect to their solvent power is mandatory to find an optimal combination. By applying a model with predictive capabilities, the relative solubilities of cellulose were computed using COSMO-RS combined with different types of models describing the combinatorial contribution to the chemical potential. The results are in good qualitative agreement with those from the scarce experimental data available in the literature. On the basis of these calculations, insight into the solvation mechanism within these systems was obtained. A screening of more than 2000 ionic liquids pointed to the anion as mainly being responsible for the respective dissolving power, suggesting some new ionic liquids as potential candidates for cellulose dissolution.