To eliminate the problem of the aging of cellulose insulation in the manufacturing stage, a new drying method is being developed based on the use of methanol vapors. Previous studies have shown that the complete removal of methanol from the cellulose insulation after the drying process is very difficult. Therefore, it is necessary to check how the remaining methanol after drying affects the properties of both the cellulose materials and mineral oil. To conduct such studies, it is necessary to know the methanol content in oil that can be expected depending on its initial content in the cellulose materials and the temperature of the insulation system. Therefore, the main goal of this work is to develop methanol equilibrium curves for oil–paper insulation. To achieve the assumed goal, three-stage studies were conducted. A gas chromatograph equipped with a flame ionization detector was used in all stages of these studies. The gas partition coefficient between oil and air was determined for a temperature of 70 °C. The key experimental finding was the development of methanol equilibrium curves for oil–paper insulation. Thanks to this achievement, it is possible to estimate the methanol content in cellulose materials and mineral oil depending on the insulation temperature. Such data are necessary, among others, to plan appropriate studies aimed at assessing the impact of methanol content on the dielectric and physicochemical properties of these materials, important from the point of view of the operation of power transformers.