The matroid toric-ideal quadratic Gröbner-basis conjecture

Let $M$ be a matroid and let $I_M$ be its toric ideal, the kernel of the map sending each base variable $y_B$ to the corresponding squarefree monomial. The matroid quadratic Gröbner-basis conjecture. The toric ideal $I_M$ has a Gröbner basis consisting of quadratic binomials. This is presented as a variant of White's conjecture and would imply the normality Gröbner-basis conjecture for toric varieties $Y_M$ arising from matroids. The source states that it remains open.