  The recent detection of a neutron star binary through gravitational waves,
GW170817, has offered another source of information about the properties of
cold supranuclear matter. Information from the signal emitted before the
neutron stars merged has been used to study the equation of state of these
bodies, however, any complementary information included in the signal emitted
after the merger has been lost in the detector noise. In this paper we
investigate the prospects of studying GW170817-like post-merger signals with
future gravitational-wave detectors. We first compute the expected properties
of the possible GW170817 post-merger signal using information from pre-merger
analyses. We then quantify the required improvement in detector sensitivity in
order to extract key features of the post-merger signal. We find that if we
observe a signal of similar strength to GW170817 when the aLIGO detectors have
been improved by $\sim 2-3$ times over their design sensitivity in the kHz
regime, we will be able to extract the dominant frequency component of the
post-merger. With further improvements and next-generation detectors we will
also be able to extract subdominant frequencies. We conclude that post-merger
signals could be brought within our reach in the coming years given planned
detector upgrades, such as A+, Voyager, and the next-generation detectors.
