Recent atmospheric models for brown dwarfs suggest that the existence of clouds in substellar objects is not needed to reproduce their spectra, nor their rotationally induced photometric variability, believed to be due to the heterogeneous cloud coverage of brown dwarf atmospheres. Cloud-free atmospheric models also predict that their flux should not be polarized, as polarization is produced by the light scattering of particles in the inhomogeneous cloud layers of brown dwarf atmospheres. To shed light on this dichotomy, we monitored the linear polarization and photometric variability of the most variable brown dwarf, 2MASSJ21392676+0220226. We used FORS2 at the UT1 telescope to monitor the object in the z band for six hours, split on two consecutive nights, covering one-third of its rotation period. We obtained the Stokes parameters, and we derived its time-resolved linear polarization, for which we did not find significant linear polarization (P=0.14%{+/-}0.07%). We modeled the linear polarimetric signal expected assuming a map with one or two spot-like features and two bands using a polarization-enabled radiative transfer code. We obtained values compatible with the time-resolved polarimetry obtained for 2MASSJ21392676+0220226. The lack of significant polarization might be due to photometric variability produced mostly by banded structures or small-scale vortices, which cancel out the polarimetric signal from different regions of the dwarf's disk. Alternatively, the lack of clouds in 2MASSJ21392676+0220226 would also explain the lack of polarization. Further linear polarimetric monitoring of 2MASSJ21392676+0220226, during at least one full rotational period, would help to confirm or discard the existence of clouds in its atmosphere.