The supermassive black hole candidate at the centre of M87 drives an ultra-relativistic jet visible on kiloparsec scales, and its large mass and relative proximity allow for event horizon scale imaging with very long baseline interferometry at millimetre wavelengths (mm-VLBI). Recently, relativistic magnetohydrodynamic simulations of black hole accretion flows have proven capable of launching magnetically dominated jets. We construct time-dependent disc/jet models of the innermost portion of the M87 nucleus by performing relativistic radiative transfer calculations from one such simulation. We identify two types of models, jet-dominated or disc/jet, that can explain the spectral properties of M87, and use them to make predictions for current and future mm-VLBI observations. The Gaussian source size for the favoured sky orientation and inclination from observations of the large-scale jet is as (≃4–6 Schwarzschild radii) on current mm-VLBI telescopes, very similar to existing observations of Sgr A*. The black hole shadow, direct evidence for an event horizon, should be visible in future measurements using baselines between Hawaii and Mexico. Both models exhibit variability at millimetre wavelengths with factor of ≃2 amplitudes on year time-scales. For the low inclination of M87, the counter-jet dominates the event horizon scale millimetre wavelength emission from the jet-forming region.