We report on five compact, extremely young (< 10 Myr) and blue (β U V < −2.5, F λ = λ β ) objects observed with VLT/MUSE at redshift 3.1169, 3.235, in addition to three objects at z = 6.145. These sources are magnified by the Hubble Frontier Field galaxy clusters MACS J0416 and AS1063. Their de-lensed half light radii (R e ) are between 16 to 140 pc, the stellar masses are 1 − 20 × 10 6 M , the magnitudes are m U V = 28.8 − 31.4 (−17 < M U V < −15) and specific star formation rates can be as large as ∼ 800 Gyr −1 . Multiple images of these systems are widely separated in the sky (up to 50 ) and individually magnified by factors 3-40. Remarkably, the inferred physical properties of two objects are similar to those expected in some globular cluster formation scenarios, representing the best candidate proto-globular clusters (proto-GC) discovered so far. Rest-frame optical high dispersion spectroscopy of one of them at z = 3.1169 yields a velocity dispersion σ v 20 km s −1 , implying a dynamical mass dominated by the stellar mass. Another object at z = 6.145, with de-lensed31.4), shows a stellar mass and a star-formation rate surface density consistent with the values expected from popular GC formation scenarios. An additional star-forming region at z = 6.145, with de-lensed m U V 32, a stellar mass of 0.5 ×10 6 M and a star formation rate of 0.06 M yr −1 is also identified. These objects currently represent the faintest spectroscopically confirmed star-forming systems at z > 3, elusive even in the deepest blank fields. We discuss how proto-GCs might contribute to the ionization budget of the universe and augment Lyα visibility during reionization. This work underlines the crucial role of JWST in characterizing the restframe optical and near-infrared properties of such low-luminosity high−z objects.