  The formation of globular clusters (GC), with their multiple stellar
generations, is still an unsolved puzzle. Thus, interest is rising on the
possibility to detect their precursors at high redshift, hence directly
witnessing their formation. A simple set of assumptions are empirically
justified and then used to predict how many such precursors formed between
redshift 3 and 10 could actually be detected by the NIRCam instrument on board
of JWST. It is shown that the near power-law shape of the rest-frame UV
continuum of young globular cluster precursors (GCP) implies that both colours
and luminosities in NIRCam long-wavelength passbands depend remarkably weakly
on formation redshift. Thus, the predicted number counts depend only little on
the actual formation redshifts in the mentioned range, with the exception of
the bluest passbands for which counts can be strongly suppressed by
intergalactic absorption along the line of sight. Instead, counts depend
strongly on the actual mass of GCPs, in such a way that one NIRCam pointing
should detect of the order of 10 GCPs to mag$\sim 30$ if their mass
distribution was the same of today GCs, or over 1,000 if their mass was 10
times higher. Therefore, GCP number counts will set fairly tight constraints on
the initial mass of GCs. An encouraging agreement with the number density of
candidate GCPs at $z=6-8$, revealed by the Hubble Frontier Fields (HFF)
program, suggests that their initial mass could be at least 4 times higher than
that of their local descendants if all were to end up as GCs.
