Nuclear clusters (NCs) are common stellar systems in the centres of galaxies. Yet, the physical mechanisms involved in their formation are still debated. Using a parsec-resolution hydrodynamical simulation of a dwarf galaxy, we propose an updated formation scenario for NCs. In this `wet migration scenario', a massive star cluster forms in the gas-rich disc, keeping a gas reservoir, and growing further while it migrates to the centre via a combination of interactions with other substructures and dynamical friction. A wet merger with another dense cluster and its own gas reservoir can occur, although this is not a prerequisite for the actual formation of the NC. The merging process does significantly alter the properties of the NC (mass, morphology, star formation history), also quenching the ongoing local star formation activity, thus leading to interesting observational diagnostics for the physical origin of NCs. A population of lower mass clusters co-exist during the simulation, but these are either destroyed via tidal forces, or have high angular momentum preventing them to interact with the NC and contribute to its growth. The proposed updated scenario emphasizes the role of gas reservoirs associated with the densest star clusters formed in a gas-rich low-mass galaxy.