While many properties of the magnetic compass of migratory birds are satisfactory explained within the chemical model of magnetoreception, its extreme sensitivity to radiofrequency magnetic fields remains a mystery. Apparently, this difficulty could be overcome if the magnetoreceptor model were augmented with a magnetite nanoparticle, which would amplify the magnetic field at the position of the magneto-sensitive cryptochrome molecule. However, comparison of the radio-frequency power used in the experiment with intrinsic magnetization noise of such a particle, estimated from the theory of fluctuations, shows that the required sensitivity cannot be reached with realistic parameters of iron-oxide nanocrystals.