[en] Lepton flavour violation is not allowed by the Standard Model (SM), yet it has been observed in neutrinos. The physics responsible for neutrino oscillations and masses is still unknown and it may allow charged lepton flavour violation (CLFV). Evidence for CLFV processes, strongly suppressed according to the SM, would shed light on the nature of New Physics. Studies towards a search for CLFV will be presented using 13 TeV data collected between 2015 and 2017 by the ATLAS detector. The analysis investigates the decay of a top quark into a pair of opposite-sign different-flavour leptons and a up-type quark. The search, never performed before in this channel, benefits from the clear signature and the large top-quark pair production cross section in proton-proton collision at the Large Hadron Collider. The theoretical description is given in the framework of an effective field theory, allowing for a model-independent search.