Jon Heyman writes that, despite today's trade for Marlon Byrd, the Pirates are still interested in Justin Morneau. It's clear from today's press conference that the Pirates consider Starling Marte's injury to be fairly significant, so it's possible that they're thinking of the Byrd acquisition as one that just gets them back to where they were when Marte was healthy. Even then, an upgrade at the corners would have made sense.
Heyman reports that the Twins are willing to pick up salary, and the holdup is their return. As I've written before, I wouldn't expect Morneau to fetch much.