Context. Next-generation wide-field optical polarimeters such as Wide-Area Linear Optical Polarimeters (WALOPs) have a field of view (FoV) of tens of arcminutes. Wide-field polarimetric flat sources are essential to the efficient and accurate calibration of these instruments. However, no established wide-field polarimetric standard or flat sources exist at present. Aims. This study tests the feasibility of using the polarized sky patches of the size of around 10 × 10 arcminutes², at a distance of up to 20° from the Moon, on bright-Moon nights as a wide-field linear polarimetric flat source. Methods. We observed 19 patches of the sky adjacent to the bright-Moon with the RoboPol instrument in the SDSS-r broadband filter. These patches were observed on five nights within two days of the full-Moon across two RoboPol observing seasons. Results. We find that for 18 of the 19 patches, the uniformity in the measured normalized Stokes parameters q and u is within 0.2%, with 12 patches exhibiting uniformity within 0.07% or better for both q and u simultaneously, making them reliable and stable wide-field linear polarization flats. Conclusions. We demonstrate that the sky on bright-Moon nights is an excellent wide-field linear polarization flat source. Various combinations of the normalized Stokes parameters q and u can be obtained by choosing suitable locations of the sky patch with respect to the Moon.