We report on high angular resolution polarimetric observations of the nearby radio galaxy M87 using the Very Long Baseline Array at 24 GHz (λ = 1.3 cm) and 43 GHz (λ = 7 mm) in 2017–2018. New images of the linear polarization substructure in the nuclear region are presented, characterized by a two-component pattern of polarized intensity and smooth rotation of the polarization plane around the 43 GHz core. From a comparison with an analogous dataset from 2007, we find that this global polarization pattern remains stable on a time interval of 11 yr, while showing smaller month-scale variability. We discuss the possible Faraday rotation toward the M87 nucleus at centimeter to millimeter wavelengths. These results can be interpreted in a scenario where the observed polarimetric pattern is associated with the magnetic structure in the confining magnetohydrodynamic wind, which also serves as the source of the observed Faraday rotation.