Aims. The central region of the giant low-surface-brightness galaxy Malin 1 has long been known to have a complex morphology, with evidence of a bulge, disc, and potentially a bar hosting asymmetric star formation. In this work, we use VLT/MUSE data to resolve the central region of Malin 1 in order to determine its structure. Methods. We used careful light profile fitting in every image slice of the datacube to create wavelength-dependent models of each morphological component, from which we were able to cleanly extract their spectra. We then used the kinematics and emission line properties from these spectra to better understand the nature of each component extracted from our model fitting. Results. We report the detection of a pair of distinct sources at the centre of this galaxy with a separation of ∼1.05″, which corresponds to a separation on sky of ∼1.9 kpc. The radial velocity data of each object confirm that they both lie in the kinematic core of the galaxy. An analysis of the emission lines reveals that the central compact source is more consistent with being ionised through star formation and/or a LINER, while the off-centre compact source lies closer to the separation between star-forming galaxies and active galactic nuclei. Conclusions. This evidence suggests that the centre of Malin 1 hosts either a bar with asymmetric star formation or two distinct components. In the latter scenario, we propose two hypotheses for the nature of the off-centre compact source-it could either be a star-forming clump, containing one or more star clusters, that is in the process of falling into the core of the galaxy and eventually merging with the central nuclear star cluster, or it could be a clump of gas falling into the centre of the galaxy from either outside or from the disc and triggering star formation there.