ABSTRACT We present a multiwavelength analysis of two highly magnified strong gravitationally lensed galaxies, CLASS B0712+472 and CLASS B1608+656, at redshifts 1.34 and 1.394, respectively, using new VLBI (very long baseline interferometry) and archival Hubble Space Telescope observations. We reconstruct the positions of the radio and optical emissions with their uncertainties using Monte Carlo sampling. We find that in CLASS B0712+472 the optical and radio emissions are co-spatial within 2 ± 5 mas (17 ± 42 pc at redshift of 1.34). But, in CLASS B1608+656, we reconstruct an optical–radio offset of 25 ± 16 mas (214 ± 137 pc at redshift of 1.394), among the smallest offsets measured for an AGN (active galactic nucleus) at such high redshift. The spectral features indicate that CLASS B1608+656 is a post-merger galaxy, which, in combination with the optical–VLBI offset reported here, makes CLASS B1608+656 a promising candidate for a high- z offset–AGN. Furthermore, the milliarcsecond angular resolution of the VLBI observations combined with the precise lens models allow us to spatially locate the radio emission at 0.05 mas precision (0.4 pc) in CLASS B0712+472, and 0.009 mas precision (0.08 pc) in CLASS B1608+656. The search for optical–radio offsets in high redshift galaxies will be eased by the upcoming synoptic all-sky surveys, including Extremely Large Telescope and Square Kilometre Array, which are expected to find ∼105 strongly lensed galaxies, opening an era of large strong lensing samples observed at high angular resolution.