  The heaviest elements in the Universe are synthesized through rapid neutron
capture ($r$-process) in extremely neutron rich outflows. Neutron star mergers
were established as an important $r$-process source through the multi-messenger
observation of GW170817. Collapsars were also proposed as a potentially major
source of heavy elements; however, this is difficult to probe through optical
observations due to contamination by other emission mechanisms. Here we present
observational constraints on $r$-process nucleosynthesis by collapsars based on
radio follow-up observations of nearby long gamma-ray bursts. We make the
hypothesis that late-time radio emission arises from the collapsar wind ejecta
responsible for forging $r$-process elements, and consider the constraints that
can be set on this scenario using radio observations of a sample of Swift/BAT
GRBs located within 2 Gpc. No radio counterpart was identified in excess of the
radio afterglow of the GRBs in our sample, limiting the collapsar $r$-process
contribution to $\lesssim0.2$ M$_\odot$ under the models we considered, with
constant circum-merger densities giving more stringent constraints. While our
results are in tension with collapsars being the majority $r$-process
production sites, the ejecta mass and velocity profile of collapsar winds is
not yet well modeled. As such, our results are currently subject to large
uncertainties, but further theoretical work could greatly improve them.
