  Spatially homogeneous cosmological spacetimes, evolving in the presence of a
positive cosmological constant and matter satisfying some reasonable energy
conditions, typically approach the de Sitter geometry asymptotically (at least
locally). In this work, we propose an alternate way to characterize this
phenomena. We focus on a subset of such models admitting a generalized
Kerr-Schild representation. We argue that the functions which define such a
representation can be chosen, such that, their asymptotic behavior make the
evolution towards the de Sitter spacetime manifest through the representation.
We verify our claim for the Kantowski-Sachs family of cosmological spacetimes.
