In this paper, a detailed study to probe the top quark Flavour-Changing Neutral Currents (FCNC) tqγ and tqZ at the future e − e + collider FCC-ee in three different center-of-mass energies of 240, 350 and 500 GeV is presented. A set of useful variables are proposed and used in a multivariate technique to separate signal e − e + → Z/γ → tq (tq) from standard model background processes. The study includes a fast detector simulation based on the delphes package to consider the detector effects. The 3σ discovery regions and the upper limits on the FCNC branching ratios at 95% confidence level (CL) in terms of the integrated luminosity are presented. It is shown that with 300 fb −1 of integrated luminosity of data, FCC-ee would be able to exclude the effective coupling strengths above O(10 −4 − 10 −5 )which is corresponding to branching fraction of O(0.01 − 0.001)%. We show that moving to a high-luminosity regime leads to a significant improvement on the upper bounds on the top quark FCNC couplings to a photon or a Z boson.