A radio-emitting tidal disruption event (AT2019dsg) is proposed as a likely counterpart of the IceCube neutrino event IceCube-191001A. In this work we have revisited the Fermi-LAT data in the direction of the neutrino and confirmed no signal at the site of AT2019dsg. Instead, at the edge of the 90% confidential level error region of this neutrino there is a γ-ray transient source spatially coincident with the blazar GB6 J2113+1121. When IceCube-191001A arriving, GB6 J2113+1121 is undergoing the strongest γ-ray flare since the start of the Fermi-LAT operation, with a variability amplitude as high as over 20-times. Meanwhile, violent infrared and optical flares of GB6 J2113+1121, unobserved before, have been simultaneously detected. Motivated by the spatial and temporal coincidence, we suggest that GB6 J2113+1121 is a candidate of the counterpart of IceCube-191001A. The jet properties of GB6 J2113+1121 are investigated, which are found to be comparable with that of the neutrino-emitting blazars (candidates). A specific analysis of archival IceCube data in this direction and future observations would put a further constraint on the origin of the neutrino.