The measurement of the Higgs self-interaction is an important test of the Standard Model (SM) electroweak symmetry breaking sector. Sensitivity to the Higgs self-coupling for m$_{H}$ = 125 GeV is evaluated through the measurement of the non-resonant di-Higgs production final states in proton-proton collisions at a future hadron collider with a center-of-mass energy of 100 TeV. The parton-level generation of the signal and the backgrounds is performed by using MadGraph5$\_$aMC@NLO; then, the Delphes framework is used for a fast parametrization of the FCC-hh detector response. The considered decay channels are $HH \to VVb\bar{b}$, where $V=Z,W$. For the non-resonant SM signal in an ideal detector parametrization, a precision of O(10%-20%) on the SM cross-section can be estimated in the $b\bar{b}ZZ(4l)$ and $b\bar{b}WW(l\nu jj)$, respectively, corresponding to a precision of O(14%-40%) on the Higgs trilinear coupling.