A minimal model based on the Covariant Physical Couplings (CPC) framework for gravity is proposed. The CPC framework is based on the assumptions of a metric-compatible four-dimensional Riemannian manifold where a covariantly conserved stress-energy tensor acts as source of the field equations which are formally the same as Einstein field equations, but where the couplings {G, c, Λ} are allowed to vary simultaneously. The minimal CPC model takes Λ as a genuine constant while c and G vary in an entangled way that is consistent with Bianchi identity and the aforementioned assumptions. The model is constrained using the most recent galaxy cluster gas mass fraction observational data. Our result indicates that the functions c(z) and G (z) = G 0 (c/c 0 ) 4 are compatible with constant couplings for the two different parameterizations of c = c(z) adopted here.