Our main aim in this paper is to present detailed studies to probe the top quark flavor changing neutral current (FCNC) interactions at tqg, tqγ, tqH and tqZ(σ µν , γµ) vertices in the triple-top signal pp → tt t ( tt t) at the high energy proposal of Large Hadron Collider (HE-LHC) and future circular hadron-hadron collider (FCC-hh). To this end, we investigate the production of three top quarks which arises from the FCNC couplings taken into account the fast simulation at √ s = 27 TeV of HE-LHC and 100 TeV of FCC-hh considering the integrated luminosities of 10, 15 and 20 ab −1 . All the relevant backgrounds are considered in a cut based analysis to obtain the limits on the anomalous couplings and the corresponding branching ratios. The obtained exclusion limits on the coupling strengths and the branching ratios are summarized and compared in details with the results in the literature, namely the most recent direct LHC experimental limits and HL-LHC projections as well. We show that, for higher energy phase of LHC, a dedicated search for the top quark FCNC couplings can achieve much better sensitivities to the triple-top signal than other top quark production scenarios. We found that the limits for the branching ratios of tqg and tqH transitions could reach an impressive sensitivity and the obtained 95% CL limits are at least three orders of magnitude better than the current LHC experimental results as well as the existing projections of HL-LHC. CONTENTS I. Introduction and Motivations 1 II. Theoretical framework and assumptions 3 III. Analysis strategy and numerical calculations 3 A. The tqX signal and SM backgrounds 4 B. The simulation and detector effects 5 IV. Statistical method for the tqX FCNC analysis 6 A. The signal and background analysis and distributions at HE-LHC 6 B. The signal and background analysis and distributions at FCC-hh 7 V. Analysis results and 95% confidence level limits at HE-LHC and FCC-hh colliders 8 VI. Summary and conclusions 10 Acknowledgments 11 References 12 I.