  Active droplets can swim spontaneously in viscous flows as a result of the
non-linear convective transport of a chemical solute produced at their surface
by the Marangoni and/or phoretic flows generated by this solute's inhomogeneous
distribution, provided the ratio of convective-to-diffusive solute transport,
or P\'eclet number $\mbox{Pe}$ is large enough. As the result of their net
buoyancy, active drops typically evolve at a small finite distance $d$ from
rigid boundaries. Yet, existing models systematically focus on unbounded flows,
ignoring the effect of the wall proximity on the intrisically-nonlinear nature
of their propulsion mechanism. In contrast, we obtain here a critical insight
on the propulsion of active drops near walls by analysing their stability to
non-axisymmetric perturbations and the resulting emergence of self-propulsion
along the wall with no limiting assumption on the wall-distance $d$. Dipolar or
quadrupolar axisymmetric (levitating) base states are identified depending on
$d$ and $\mbox{Pe}$. Perhaps counter-intuitively, a reduction in the drop-wall
separation $d$ is observed to destabilize these modes and to promote
self-propulsion, as a result from the confinement-induced localisation of the
chemical gradients driving the motion. In addition, quadrupolar states are more
unstable than their dipolar counterparts due to the redistribution of the
chemical perturbation by the base flow, favouring the emergence of stronger
slip forcing on the drop surface.
