Even though plenty of symbiotic stars (SySts) have been found in the Galactic field and nearby galaxies, not a single one has ever been confirmed in a Galactic globular cluster (GC). We investigate the lack of such systems in GCs for the first time by analysing 144 GC models evolved with the MOCCA code, which have different initial properties and are roughly representative of the Galactic GC population. We focus here on SySts formed through the wind-accretion channel, which can be consistently modelled in binary population synthesis codes. We found that the orbital periods of the majority of such SySts are sufficiently long (${gtrsim10^3}$ d) so that, for very dense GC models, dynamical interactions play an important role in destroying their progenitors before the present day (${sim11-12}$ Gyr). In less dense GC models, some SySts are still predicted to exist. However, these systems tend to be located far from the central parts (${gtrsim70}$ per cent are far beyond the half-light radius) and are sufficiently rare (${lesssim1}$ per GC per Myr), which makes their identification rather difficult in observational campaigns. We propose that future searches for SySts in GCs should be performed in the outskirts of nearby low-density GCs with sufficiently long half-mass relaxation times and relatively large Galactocentric distances. Finally, we obtained spectra of the candidate proposed in $omega$ Cen (SOPS IV e-94) and showed that this object is most likely not a SySt.
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