  In this paper, we study the triple top quark production at the future
high-energy proton-proton colliders to probe the four-fermion interactions
involving three top quarks. We employ the Standard Model Effective Field Theory
(SMEFT) to find the upper limits at $95\%$ CL on the Wilson coefficients of
these kinds of four-fermion operators. We consider a detailed analysis with a
unique signal signature of two same-sign leptons. A full simulation chain
includes all the relevant backgrounds, realistic detector simulations and a
cut-based technique are taken into account. This study is presented for the
HE-LHC working at the center of mass energy of 27 TeV with 15~ab$^{-1}$ and
FCC-hh working at the center of mass energy of 100 TeV with 30~ab$^{-1}$. We
show that the future high-energy proton-proton colliders could reach an
impressive sensitivity to four-fermion contact interactions involving three top
quarks.
