Let $i : U \to X$ be a quasi-compact open immersion of schemes. Under which conditions is the natural map

$i_* M \otimes i_* N \to i_* (M \otimes N)$

for all $M,N \in \text{Qcoh}(U)$ an isomorphism? We may assume that $X=\text{Spec}(A)$ is affine. If $U$ is affine, then we may reduce to the case $M=N=\mathcal{O}_U$ (using presentations) and use that $i^{\#}$ is a flat epimiorphism to get an affirmative answer. If there are counterexamples for general $U$, what conditions are sufficient?