If $\mathcal{E}$ is a locally free sheaf and $j:U\to X$ is an open immersion, is $j_*j^* \mathcal{E}$ also locally free?

Question

Let $j:U\to X$ be an open immersion of schemes (feel free to suppose that they're algebraic varieties or even other conditions) and $\mathcal{E}$ be a locally free sheaf on $X$.

Is it true that $j_*j^* \mathcal{E}$ is locally free on $X$? If not, is it coherent?

I know that the direct image of a locally free isn't in general locally free. But perhaps the fact that we're taking the direct image of the restriction of a locally free sheaf plays a role here?