Not necessarily rebuilding candidate, but a retooling one: Portland.
Aldridge is the linchpin of that roster. If he stays in Portland, then I think they continue to make moves to somehow improve and challenge in the West.
But if Aldridge signs elsewhere, I think there's a lot that could happen. Wes Matthews might not be brought back. Afflalo might opt out for a bigger payday. Robin Lopez could be wooed away by another team. The Blazers might opt to recast the roster around Lillard, McCollum, Batum, and Meyers Leonard.