We examine whether the super star‐forming (super‐SF) clumps (R∼ 1–3 kpc; M∼ 108– 109.5 M⊙) now known to be a key component of star‐forming galaxies at z∼ 2 could be the formation sites of the locally observed old globular cluster (GC) population. We find that the stellar populations of these super‐SF clumps are excellent matches to those of local metal‐rich GCs. Moreover, this GC population is known to be associated with the bulges/thick discs of galaxies, and we show that its spatial distribution and kinematics are consistent with the current understanding of the assembly of bulges and thick discs from super‐SF clumps at high redshift. Finally, with the assumption that star formation in these clumps proceeds as a scaled‐up version of local star formation in molecular clouds, this formation scenario reproduces the observed numbers and mass spectra of metal‐rich GCs. The resulting link between the turbulent and clumpy discs observed in high‐redshift galaxies and a local GC population provides a plausible co‐evolutionary scenario for several of the major components of a galaxy: the bulge, the thick disc and one of the GC populations.