ABSTRACT IGR J17591−2342 is a new accreting millisecond X-ray pulsar that was recently discovered in outburst in 2018. Early observations revealed that the source’s radio emission is brighter than that of any other known neutron star low-mass X-ray binary (NS–LMXB) at comparable X-ray luminosity, and assuming its likely ≳6 kpc distance. It is comparably radio bright to black hole LMXBs at similar X-ray luminosities. In this work, we present the results of our extensive radio and X-ray monitoring campaign of the 2018 outburst of IGR J17591−2342. In total, we collected 10 quasi-simultaneous radio (VLA, ATCA) and X-ray (Swift–XRT) observations, which make IGR J17591−2342 one of the best-sampled NS–LMXBs. We use these to fit a power-law correlation index $β = 0.37^{+0.42}_{-0.40}$ between observed radio and X-ray luminosities (LR ∝ LXβ). However, our monitoring revealed a large scatter in IGR J17591−2342’s radio luminosity (at a similar X-ray luminosity, LX ∼1036 erg s−1, and spectral state), with LR ∼ 4 × 1029 erg s−1 during the first three reported observations, and up to a factor of 4 lower LR during later radio observations. None the less, the average radio luminosity of IGR J17591−2342 is still one of the highest among NS–LMXBs, and we discuss possible reasons for the wide range of radio luminosities observed in such systems during outburst. We found no evidence for radio pulsations from IGR J17591−2342 in our Green Bank Telescope observations performed shortly after the source returned to quiescence. None the less, we cannot rule out that IGR J17591−2342 becomes a radio millisecond pulsar during quiescence.