The Anomalous X-ray Pulsar 4U 0142+61 is the only neutron star where it is believed that one of the long searched-for 'fallback' disks has been detected in the mid-IR by Wang et al.  using Spitzer. Such a disk originates from material falling back to the NS after the supernova. We search for cold circumstellar material in the 90 GHz continuum using the Plateau de Bure Interferometer. No millimeter flux is detected at the position of 4U 0142+61, the upper flux limit is 150 μJy corresponding to the 3σ noise rms level. The re-processed Spitzer MIPS 24μm data presented previously by Wang et al.  show some indication of flux enhancement at the position of the neutron star, albeit below the 3σ statistical significance limit. At far infrared wavelengths the source flux densities are probably below the Herschel confusion limits.