  From general analyticity and unitarity requirements on the UV theory,
positivity bounds on the Wilson coefficients of the dimension-8 operators
composed of 4 fermions and two derivatives appearing in the Standard Model
Effective Field Theory have been derived recently. We explore the fate of these
bounds in the context of models endowed with a Minimal Flavor Violation (MFV)
structure, models in which the flavor structure of higher dimensional operators
is inherited from the one already contained in the Yukawa sector of the
Standard Model Lagrangian. Our goal is to check whether the general positivity
bounds translate onto bounds on the Yukawa coefficients and/or on elements of
the CKM matrix. MFV fixes the coefficients of dimension-8 operators up to some
multiplicative flavor-blind factors and we find that, in the most generic
setup, the freedom left by those unspecified coefficients is enough as not to
constrain the parameters of the renormalizable Yukawa sector. On the contrary,
the latter shape the allowed region for the former. Requiring said overall
coefficients to take natural $\mathcal{O}(1)$ values could give rise to bounds
on the Yukawa couplings. Remarkably, at leading order in an expansion in powers
of the Yukawa matrices, no bounds on the CKM entries can be retrieved.
