According to Jon Heyman of CBS Sports, Justin Morneau is not drawing significant interest right now.
Despite the Twins reportedly being interested to trade the 2006 AL MVP, not too many teams are said to be biting on the left handed slugger. The Yankees, Reds, and Rangers could use an impact bat like his, but from the right side. The Pirates have been connected to Morneau, as well as the Rays, but both teams could be put off by the ~6 million remaining on his contract as a part of his 6 year, 80 million dollar deal that he signed in 2008.
Morneau won the AL MVP in 2006, but hasn’t really been the same since. Health problems (including multiple serious concussions) have derailed his career. Since he hit .321/.375/.559 with 34 homers and 130 RBIs in 2006, he has only hit .300 in a full season once (2008.) From 2009-2011, he missed 211 games, including 93 in 2011. While his health is said to be better than it has been in the past, his production has quieted down to the point where not too many teams are interested.
Morneau is hitting a solid, if not unspectacular .273/.331/.406 with 7 homers and 52 RBIs. He would make a solid addition on a team like the Yankees who are looking for first base help. However, his high salary, diminishing returns, and unrealistic expectations from the Twins on a return for him will probably ultimately being forced to hang on to him. The players that teams do want are Josh Willingham and Glen Perkins, but Minnesota has no plans to trade either of them at this time.