We propose an alternative unification scenario where the Higgs self-coupling (λ) is determined by imposing its unification with the electroweak gauge couplings. An attractive feature of models within this scenario is the possibility to determine the Higgs boson mass by evolving λ from the electroweak–Higgs unification scale M GH down to the electroweak scale. The unification condition for the gauge (g1, g2) and Higgs couplings is written as g1 = g2 = f(λ), where [Formula: see text] being the normalization constant. Two variants for the unification condition are discussed; scenario I is defined through the linear relation: g1 = g2 = kHλ(M GH ), while scenario II assumes a quadratic relation: [Formula: see text]. Fixing kH = O(1) and the standard normalization (kY = 5/3), we obtain a Higgs boson mass value mH ≃ 190 GeV , with similar results for other normalizations such as kY = 7/4 and 3/2. However, the unification scale M GH depends on the value of kY, going from 1.8 ×1012 GeV up to 4.9 ×1014 GeV for 7/4 > kY > 3/2. Possible tests of this idea at a future linear collider and its application for determining the Higgs spectrum in the two-Higgs doublet model are also discussed. We also elaborate on these unification scenarios within the context of a six-dimensional SU (3)c× SU (3)w Gauge–Higgs unified model, where the Higgs boson arises as the extra-dimensional components of the 6D gauge fields.