We present radio observations of the tidal disruption event candidate ( TDE ) XMMSL1 J0740 - 85 spanning 592 to 875 d post X-ray discovery . We detect radio emission that fades from an initial peak flux density at 1.6 GHz of 1.19 \pm 0.06 mJy to 0.65 \pm 0.06 mJy suggesting an association with the TDE . This makes XMMSL1 J0740 - 85 at d = 75 Mpc the nearest TDE with detected radio emission to date and only the fifth TDE with radio emission overall . The observed radio luminosity rules out a powerful relativistic jet like that seen in the relativistic TDE Swift J1644+57 . Instead we infer from an equipartition analysis that the radio emission most likely arises from a non-relativistic outflow similar to that seen in the nearby TDE ASASSN-14li , with a velocity of about 10 ^ { 4 } km s ^ { -1 } and a kinetic energy of about 10 ^ { 48 } erg , expanding into a medium with a density of about 10 ^ { 2 } cm ^ { -3 } . Alternatively , the radio emission could arise from a weak initially-relativistic but decelerated jet with an energy of \sim 2 \times 10 ^ { 50 } erg , or ( for an extreme disruption geometry ) from the unbound debris . The radio data for XMMSL1 J0740 - 85 continues to support the previous suggestion of a bimodal distribution of common non-relativistic isotropic outflows and rare relativistic jets in TDEs ( in analogy with the relation between Type Ib/c supernovae and long-duration gamma-ray bursts ) . The radio data also provide a new measurement of the circumnuclear density on a sub-parsec scale around an extragalactic supermassive black hole .