We estimate the future sensitivity of the high luminosity (HL-) and high energy (HE-) modes of the Large Hadron Collider (LHC) and of a 100 TeV future circular collider (FCC-hh) to leptoquark (LQ) pair production in the muon-plus-jet decay mode of each LQ. Such LQs are motivated by the fact they provide an explanation for the neutral current $B-$anomalies. For each future collider, Standard Model (SM) backgrounds and detector effects are simulated. From these, sensitivities of each collider are found. Our measures of sensitivity are based upon a Run II ATLAS search, which we also use for validation. We illustrate with a narrow scalar ('$S3$') LQ and find that, in our channel, the HL-LHC has exclusion sensitivity to LQ masses up to 1.8 TeV, the HE-LHC up to 4.8 TeV and the FCC-hh up to 13.5 TeV.