A search for flavour-changing neutral currents in the top-quark Higgs boson sector is presented, utilizing an integrated luminosity of Lint = 140 fb1 of proton-proton collisions recorded by the ATLAS experiment at a centre-of-mass energy of s = 13 TeV. As flavour-changing neutral currents are highly suppressed in the Standard Model of particle physics, these processes are sensitive to physics beyond the Standard Model. To differentiate between signal and background, advanced reconstruction methods are employed for creating kinematic distributions. Multivariate analysis techniques are utilised to optimize the differentiation between signal and background, leading to expected upper exclusion limits on the branching ratio B (t qH) in a binned profile likelihood fit including a full set of systematic uncertainties. The obtained expected exclusion limits amount to B (t uH) < 4.1 · 104 and B (t cH) < 5.0 · 104 for the branching ratio corresponding to the utH and ctH couplings respectively.