Correlations between cosmic microwave background (CMB) temperature, polarization, and spectral distortion anisotropies can be used as a probe of primordial non-Gaussianity. Here, we perform a reconstruction of mu-distortion anisotropies in the presence of Galactic and extragalactic foregrounds, applying the so-called Constrained ILC component separation method to simulations of proposed CMB space missions (PIXIE, LiteBIRD, CORE, and PICO). Our sky simulations include Galactic dust, Galactic synchrotron, Galactic free-free, thermal Sunyaev-Zeldovich effect, as well as primary CMB temperature and mu-distortion anisotropies, the latter being added as correlated field. The Constrained ILC method allows us to null the CMB temperature anisotropies in the reconstructed mu-map (and vice versa), in addition to mitigating the contaminations from astrophysical foregrounds and instrumental noise. We compute the cross-power spectrum between the reconstructed (CMB-free) mu-distortion map and the (mu-free) CMB temperature map, after foreground removal and component separations. Since the cross-power spectrum is proportional to the primordial non-Gaussianity parameter, f(NL), on scales k similar or equal to 740 Mpc(-1), this allows us to derive f(NL)-detection limits for the aforementioned future CMB experiments. Our analysis shows that foregrounds degrade the theoretical detection limits (based mostly on instrumental noise) by more than one order of magnitude, with PICO standing the best chance at placing upper limits on scale-dependent non-Gaussianity. We also discuss the dependence of the constraints on the channel sensitivities and chosen bands. Like for B-mode polarization measurements, extended coverage at frequencies v less than or similar to 40 GHz and v greater than or similar to 400 GHz provides more leverage than increased channel sensitivity.