Takahashi's converse conjecture for contravariantly finite G-projective modules

Let $R$ be a commutative Noetherian Henselian local ring with maximal ideal $\mathfrak m$ and residue class field $k$, and let $\mathrm{mod}\,R$ denote the category of finitely generated $R$-modules. Let $\mathcal G$ be the full subcategory of $\mathrm{mod}\,R$ consisting of all G-projective $R$-modules. A subcategory is contravariantly finite if every module admits a right approximation by an object of that subcategory. Suppose that there is a nonfree G-projective $R$-module. Takahashi's conjecture. If $\mathcal G$ is contravariantly finite in $\mathrm{mod}\,R$, then $R$ is Gorenstein. This conjecture proposes a converse to the known fact that G-projective modules are contravariantly finite over Gorenstein local rings; the additional nonfree-module hypothesis excludes the vacuous case in which all G-projective modules are free.