There hasn't been a great deal of voiced interest in Justin Morneau, even though the Twins have been said to be willing to trade him. The Dodgers are the one team who have been mentioned in regards to Morneau, and more than once at that. CBS Sports' Danny Knobler has more.
Dodgers, who still want to add a bat, also have some interest in Justin Morneau— DKnobler (@DKnobler) July 27, 2012
The crux of the article is about the Cubs being a potential trade partner for the Dodgers, rather than the Twins.
Still, in the article linked above Knobler states the Dodgers "have talked about quite a few other hitters, including" both Morneau and Willingham. Far be it from me to split hairs, but I read a big difference between "have talked about" and "have interest in". Talked about means internal discussions, which virtually mean nothing. If a team has interest, then the player is a target.
Willingham's chances of being dealt are small. But it's different for Justin, and there's a lot more than performance and money that would be traded away with him.