Because keeping all of those quotes, notes, and rumors in one post is getting lengthy, let's break this down by team in separate posts. As these come in, they will be updated and reposted.
Latest status: Apparently interested
NY Post's Joel Sherman (5/25):
If I had to pick a front-runner right now for Oswalt’s services, I would pick the Angels. One AL executive firmly agreed, saying, “If I were going to Vegas, I am all-in on the Angels for Oswalt.”
The Angels have a need for a starter like Oswalt, but their farm system has been depleted in recent years.