I think any of these candidates could be realistic: Oliver Marmol, Stubby Clapp, Skip Schumaker, Matt Holliday and Carlos Beltran.
I would lean toward Marmol, and then Clapp, as most likely.
That's no big secret. Mozeliak emphasized the appeal of internal candidates in the Shildt firing announcement.
The Cardinals should do themselves a favor and open a wider net to see who might be interested. Or who might not be interested. It could be a bit of a reality check, after the box they just for their next manager (extension of the front office).
Rick Renteria wants to get back in a dugout. His camp has made that known.
No one has mentioned David Freese to my knowledge, but I bet he could be a very good modern manager if he wanted to take on the grind of the job. He would be popular with the fans, clearly, knows how to handle media and is a believer in mixing modern analytics with been-there experience. He would want to push to win big, though.
He (Freese) would want to push for championships, same as Shildt. He got a taste of that approach with the Dodgers. I don't think he would be good with always sticking to the script, if he felt like the team wasn't getting what it needed.