The rheology of spheroids has been studied intensively recently and it was shown that the presence of the extra-cellular matrix (ECM) can have significant effects on the overall behaviour of these biological systems. Collagen I can indeed be a proxy between cells and bring new intriguing effects, as its content increases. To investigate these effects further, a two-phase emulsion model is proposed including interactions between cells and the ECM. Starting with the single cell and collagen individual viscoelastic properties, the model can be tested against previously obtained data for spheroids. The model has interesting features and capabilities for it covers a variety of behaviours and uses fitting parameters such as collagen and cell concentration, as well as adhesion energy. It is shown that the final intercellular collagen content can be large as compared to the initial one, and that this increase in collagen content induces a larger packing of cells, together with a larger adhesion energy.