Smilin' Ken Rosenthal says that the Twins are not in on Oswalt, but the Dodgers are (and face the usual problem of cash and prospects).
Update: Jayson Stark confirms Rosenthal's report on the Dodgers (or Rosenthal confirms Stark's. Whatever.)
A source familiar with those discussions says the teams have swapped names this week, and continue to talk about a potential package for Oswalt.