Recent measurements carried out at comet 67P/C-G with the ${\it Rosetta}$ probe revealed that molecular oxygen, O$_2$, is the fourth most abundant molecule in comets. Models show that O$_2$ is likely of primordial nature, coming from the interstellar cloud from which our Solar System was formed. However, gaseous O$_2$ is an elusive molecule in the interstellar medium with only one detection towards quiescent molecular clouds, in the $\rho$ Oph A core. We perform a deep search for molecular oxygen, through the $2_1 - 0_1$ rotational transition at 234 GHz of its $^{16}$O$^{18}$O isotopologue, towards the warm compact gas surrounding the nearby Class 0 protostar IRAS 16293--2422 B with the ALMA interferometer. The targeted $^{16}$O$^{18}$O transition is surrounded by two brighter transitions at $\pm 1$ km s$^{-1}$ relative to the expected $^{16}$O$^{18}$O transition frequency. After subtraction of these two transitions, residual emission at a 3$\sigma$ 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 O$_2$ column density for two excitation temperatures $T_{\rm ex}$ of 125 and 300 K, as indicated by other molecules, in order to compare the O$_2$ abundance between IRAS16293 and comet 67P/C-G. Assuming that $^{16}$O$^{18}$O is not detected and using methanol CH$_3$OH as a reference species, we obtain a [O$_2$]/[CH$_3$OH] abundance ratio lower than $2-5$, depending on the assumed $T_{\rm ex}$, a three to four times lower abundance than the [O$_2$]/[CH$_3$OH] ratio of $5-15$ found in comet 67P/C-G. Such a low O$_2$ abundance could be explained by the lower temperature of the dense cloud precursor of IRAS16293 with respect to the one at the origin of our Solar System that prevented an efficient formation of O$_2$ in interstellar ices.< Réduire