  The forward LHCb acceptance opens interesting possibilities of studying
precision Standard Model hard processes in a kinematical region beyond the
reach of ATLAS and CMS. In this paper we perform a feasibility study for
cross-section measurements of top quark pairs with the LHCb detector, with an
analysis of signal and background rates for selected final states, and
determine the potential precision achievable at $\sqrt{s} =$ 7 and 14~TeV. We
then study the dependence of theoretical uncertainties on the pseudorapidity
distribution of top quarks produced in pair production at NLO, and observe that
a cross-section measurement at high pseudorapidity has enhanced sensitivity to
probe the high-$x$ gluon PDF as compared to measurements in the central-region.
Based on simulated pseudodata, the impact of a 14~TeV cross-section measurement
on the gluon PDF and charge asymmetry is quantified.
