We study the off-shell Higgs data in the process pp→h(∗)→Z(∗)Z(∗)→4ℓ, to constrain deviations of the Higgs couplings. We point out that this channel can be used to resolve the long- and short-distance contributions to Higgs production by gluon fusion and can thus be complementary to pp→htt¯ in measuring the top Yukawa coupling. Our analysis, performed in the context of Effective Field Theory, shows that current data do not allow one to draw any model-independent conclusions. We study the prospects at future hadron colliders, including the high-luminosity LHC and accelerators with higher-energy, up to 100 TeV. The available QCD calculations and the theoretical uncertainties affecting our analysis are also briefly discussed.