Abstract We observed the periodic radio transient GLEAM-X J162759.5-523504.3 (GLEAM-X J1627) using the Chandra X-ray Observatory for about 30 ks on 2022 January 22–23, simultaneously with radio observations from the Murchison Widefield Array, MeerKAT, and the Australia Telescope Compact Array. Its radio emission and 18 min periodicity led the source to be tentatively interpreted as an extreme magnetar or a peculiar highly magnetic white dwarf. The source was not detected in the 0.3–8 keV energy range with a 3σ upper limit on the count rate of 3 × 10⁻⁴ counts s⁻¹. No radio emission was detected during our X-ray observations either. Furthermore, we studied the field around GLEAM-X J1627 using archival European Southern Observatory and DECam Plane Survey data, as well as recent Southern African Large Telescope observations. Many sources are present close to the position of GLEAM-X J1627, but only two within the 2″ radio position uncertainty. Depending on the assumed spectral distribution, the upper limits converted to an X-ray luminosity of L _X < 6.5 × 10²⁹ erg s⁻¹ for a blackbody with temperature kT = 0.3 keV, or L _X < 9 × 10²⁹ erg s⁻¹ for a power law with photon index Γ = 2 (assuming a 1.3 kpc distance). Furthermore, we performed magneto-thermal simulations for neutron stars considering crust- and core-dominated field configurations. Based on our multiband limits, we conclude that (i) in the magnetar scenario, the X-ray upper limits suggest that GLEAM-X J1627 should be older than ∼1 Myr, unless it has a core-dominated magnetic field or has experienced fast cooling; (ii) in the white dwarf scenario, we can rule out most binary systems, a hot sub-dwarf, and a hot magnetic isolated white dwarf (T ≳ 10.000 K), while a cold isolated white dwarf is still compatible with our limits.