$A_\infty$ operad can be described both in terms of Stasheff polytopes and configuration spaces.$A_n$ operad can be described as subspace of Stasheff operad described using Stasheff polytope. Is there a model for $A_n$-operad as a configuration spaces?
At the risk of saying something stupid I'm promoting my comment to an answer. In terms of the Stasheff polytopes the $A_n$ operad sits inside the $A_\infty$ operad as the union of all faces of dimension $\leq n-2$. Another way of saying this is that the Stasheff polytopes are stratified spaces with strata indexed by rooted trees. The $A_n$ operad is defined as the union of all strata where each vertex of the tree has valence at most $n$.
Now another model of $A_\infty$ operad is given by the sequence of Fulton-MacPherson compactifications of the configuration spaces of points on the interval. The Fulton-MacPherson compactification of any space is also naturally a stratified space, with strata indexed by rooted trees, and the same prescription should work to get a configuration space model of $A_n$ operad.