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 two different center-of-mass energies of 240 and 350 GeV is presented. A set of useful variables are proposed and used in a multivariate technique to separate signal e−e+→Z/γ→tq¯ (t¯q) from Standard Model background processes. The study includes a fast detector simulation based on the delphes package to consider the detector effects. 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.