jats:p We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of jats:italicframed Dirac monopoles</jats:italic> and moduli spaces of jats:italicideal monopoles</jats:italic> . The former are Gibbons–Manton torus bundles over configuration spaces whereas the latter are obtained from them by replacing each circle factor of the fibre with a monopole moduli space by the Borel construction. They form boundary hypersurfaces in a partial compactification of the classical monopole moduli spaces. Our results follow from a general homological stability result for configuration spaces equipped with non-local data. </jats:p>