Recent measurements carried out at comet 67P/Churyumov–Gerasimenko (67P) with the Rosetta probe revealed that molecular oxygen, O₂, is the fourth most abundant molecule in comets. Models show that O₂ is likely of primordial nature, coming from the interstellar cloud from which our solar system was formed. However, gaseous O₂ is an elusive molecule in the interstellar medium with only one detection towards quiescent molecular clouds, in the ρ Oph A core. We perform a deep search for molecular oxygen, through the 2₁−0₁ rotational transition at 234 GHz of its ¹⁶O¹⁸O isotopologue, towards the warm compact gas surrounding the nearby Class 0 protostar IRAS 16293–2422 B with the ALMA interferometer. We also look for the chemical daughters of O₂, HO₂, and H₂O₂. Unfortunately, the H₂O₂ rotational transition is dominated by ethylene oxide c-C₂H₄O while HO₂ is not detected. The targeted ¹⁶O¹⁸O transition is surrounded by two brighter transitions at ± 1 km s⁻¹ relative to the expected ¹⁶O¹⁸O transition frequency. After subtraction of these two transitions, residual emission at a 3σ level remains, but with a velocity offset of 0.3−0.5 km s⁻¹ relative to the source velocity, rendering the detection “tentative”. We derive the O₂ column density for two excitation temperatures T_ex of 125 and 300 K, as indicated by other molecules, in order to compare the O₂ abundance between IRAS 16293 and comet 67P. Assuming that ¹⁶O¹⁸O is not detected and using methanol CH₃OH as a reference species, we obtain a [O₂]/[CH₃OH] abundance ratio lower than 2−5, depending on the assumed T_ex, a three to four times lower abundance than the [O₂]/[CH₃OH] ratio of 5−15 found in comet 67P. Such a low O₂ abundance could be explained by the lower temperature of the dense cloud precursor of IRAS 16293 with respect to the one at the origin of our solar system that prevented efficient formation of O₂ in interstellar ices.