We analyze the highest-resolution millimeter continuum and near-infrared ( NIR ) scattered-light images presented to date of the circumbinary disk orbiting V4046 Sgr , a \sim 20 Myr old actively accreting , close binary T Tauri star system located a mere 72.4 pc from Earth . We observed the disk with the Atacama Large Millimeter/submillimeter Array ( ALMA ) at 870 \micron during Cycle 4 , and we analyze these data in conjunction with archival NIR ( H band ) polarimetric images obtained with SPHERE/IRDIS on the ESO Very Large Telescope . At 0.3 ^ { \prime \prime } ( 20 au ) resolution , the 870 \micron image reveals a marginally resolved ring that peaks at \sim 32 au and has an extension of \sim 90 au . We infer a lower limit on dust mass of \sim 60.0 M _ { \oplus } within the 870 \micron ring , and confirm that the ring is well aligned with the larger-scale gaseous disk . A second , inner dust ring is also tentatively detected in the ALMA observations ; its position appears coincident with the inner ( \sim 14 au radius ) ring detected in scattered light . Using synthetic 870 \micron and H-band images obtained from disk-planet interaction simulations , we attempt to constrain the mass of the putative planet orbiting at 20 au . Our trials suggest that a circumbinary Jovian-mass planet may be responsible for generating the dust ring and gap structures detected within the disk . We discuss the longevity of the gas-rich disk orbiting V4046 Sgr in the context of the binary nature of the system .