I think some clubs are pretty reserved in their comments, so I'm not sure the absence of public rumor necessarily proves that a team isn't interested or isn't quietly negotiating with an agent. The media always speculates on the big market teams, so there's a decent chance that public rumor will tend to mention a team like the Cubs more than some others.
Is there any chance the Cardinals might not have an interest? They may view themselves as having a very good team that has a shot. They still had a real shot to catch the Cubs into mid-September. They added Ozuna, who just posted a .924 season and having just turned 27 may have just hit his prime. Might they not think that by adding Ozuna and Darvish, while the Cubs were losing Davis and Arrieta, that they might not have at least a reasonable shot to pass the Cubs up? Given that Ozuna is not expensive, and they had cash to take on Stanton's contract, shouldn't they have some $$ left to spend?
Of course I'm not saying they're after Darvish, just that it's probably not as simple as Cubs or Twins and there's really nowhere else for Darvish to go. Who knows who will eventually pop up and sign him?