An improved method and system for cleaning a cylinder of a printing press. One method involves soaking a strip of cleaning fabric on a press with a low volatility organic compound solvent. Excess solvent, if any, is removed to place the strip of cleaning fabric in functional equilibrium with the solvent. The cleaning fabric is then used to clean a cylinder. Alternatively, the strip of cleaning fabric is soaked on site by contacting the strip of cleaning fabric with the solvent and wrapping the strip of cleaning fabric into a cleaning fabric supply roll. The cleaning fabric is then brought in engagement with a printing press having a cylinder to be cleaned without disposing a sleeve around the fabric roll and without substantially disturbing the distribution of the solvent in the fabric roll and detrimentally affecting the cleaning ability of the fabric.