  Within a generalized parton model approach, with inclusion of spin and
intrinsic transverse momentum effects, we show how the latest, highly precise,
midrapidity data on the transverse single spin asymmetry measured in
$pp\to\pi^0\, X$ by the PHENIX Collaboration at RHIC [1], can be used to get a
first estimate on the still poorly known gluon Sivers distribution. To this end
we also adopt the present information on the quark Sivers functions, as
extracted from semi-inclusive deeply inelastic scattering data. This analysis
updates a previous study by some of us where a first bound on this distribution
was obtained [2].
