In this paper, a detailed study to probe the top quark Flavour-Changing Neutral Currents (FCNC) tqγ and tqZ at the future 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 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 of integrated luminosity of data, FCC-ee would be able to exclude the effective coupling strengths above which is corresponding to branching fraction of %. 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.