@Chris's comment, posted as an answer by request (made CW to avoid reputation):

A sufficient condition is that $U$ is affine. Indeed $\mathcal I$ fits in an s.e.s. $0 \to \mathcal K \to \mathcal O^n \to \mathcal I \to 0$ and $H^1(U, \mathcal K) = 0$ for $U$ affine.