  We show that the three-dimensional asymptotically linear dilaton background
that arises in the near-horizon decoupling region of NS5-branes compactified on
$T^4$ admits boundary conditions that lead to an infinite set of symmetries.
The associated conserved charges, which implement field-dependent coordinate
transformations, are found to be identical to the corresponding generators in a
symmetric product orbifold of $T\bar T$ - deformed CFTs. Their algebra is a
non-linear modification of the $\mathrm{Virasoro \times Virasoro}$ algebra,
which precisely coincides with the algebra of the "unrescaled" symmetry
generators in $T\bar T$-deformed CFTs. This further strengthens a previously
proposed link between the single-trace $T\bar T$ deformation and compactified
little string theory.
