We consider a continuous, infinitely divisible random field in $\mathbb{R}^d$, $d=1,2,3$, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields we compute the asymptotic probability that the excursion set at level $x$ contains some rotation of an object with fixed radius as $x\to\infty$. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.

Keywords: convolution equivalence; excursion set; infinite divisibility; Lévy-based modelling