  Merging galaxy clusters produce low Mach number shocks in the intracluster
medium. These shocks can accelerate electrons to relativistic energies that are
detectable at radio frequencies. MACS J0744.9+3927 is a massive ($M_{500} =
(11.8 \pm 2.8) \times 10^{14} M_{\odot}$), high-redshift ($z=0.6976$) cluster
where a Bullet-type merger is presumed to have taken place. Sunyaev-Zel'dovich
maps from MUSTANG indicate that a shock, with Mach number $\mathcal{M} =
1.0-2.9$ and an extension of $\sim 200$ kpc, sits near the centre of the
cluster. The shock is also detected as a brightness and temperature
discontinuity in X-ray observations. To search for diffuse radio emission
associated with the merger, we have imaged the cluster with the LOw Frequency
ARray (LOFAR) at 120-165 MHz. Our LOFAR radio images reveal previously
undetected AGN emission, but do not show clear cluster-scale diffuse emission
in the form of a radio relic nor a radio halo. The region of the shock is on
the western edge of AGN lobe emission from the brightest cluster galaxy.
Correlating the flux of known shock-induced radio relics versus their size, we
find that the radio emission overlapping the shocked region in MACS
J0744.9+3927 is likely of AGN origin. We argue against the presence of a relic
caused by diffusive shock acceleration and suggest that the shock is too weak
to accelerate electrons from the intracluster medium.
