We present a study to examine the sensitivity of a future $e^{-} e^{+}$ collider to the anomalous top flavour-changing neutral current (FCNC) to the gluon. To separate signal from background a multivariate analysis is performed on top-quark pair and background events, where one top quark is considered to follow the dominant Standard Model (SM) decay, $t → Wb$, and the other top decays through FCNC, $t→ qg$, where $q$ is a $u-$ or a $c-$quark. The analysis of fully-hadronic FCNC decay of the $t \bar{t}$ pair is also presented. The $95\%$ confidence level limits on the top-quark anomalous couplings are obtained for different values of the center-of-mass energies and integrated luminosities. ; Comment: 14 pages, 8 figures, two tables