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Debris discs are commonly swathed in gas which can be observed in UV, in fine structure lines in FIR, and in resolved maps of CO emission. Carbon and oxygen are overabundant in such gas, but it is severely depleted in hydrogen. As a consequence, its ionisation fraction is remarkably high, suggesting magnetohydrodynamic (MHD) processes may be important. In particular, the gas may be subject to the magnetorotational instability (MRI), and indeed recent modelling of $\beta$ Pictoris requires an anomalous viscosity to explain the gas's observed radial structure. In this paper we explore the possibility that the MRI is active in debris-disc gas and responsible for the observed mass transport. We find that non-ideal MHD and dust-gas interactions play a subdominant role, and that linear instability is viable at certain radii. However, owing to low gas densities, the outer parts of the disc could be stabilised by a weak ambient magnetic field, though it is difficult to constrain such a field. Even if the MRI is stabilised by too strong a field, a magnetocentrifugal wind may be launched in its place and this could lead to equivalent (non-turbulent) transport. Numerical simulations of the vertically stratified MRI in conditions appropriate to the debris disc gas should be able to determine the nature of the characteristic behaviour at different radii, and decide on the importance of the MRI (and MHD more generally) on the evolution of these discs.