The finalists were announced Tuesday by the Baseball Writers Association of America, which votes for the award.
Goldschmidt and Molina were named as
Gold Glove winners last month, and Goldschmidt also won the Hank Aaron Award as the NL's best hitter.
The AL MVP finalists are Detroit third baseman
Miguel Cabrera, who won last year, Baltimore first baseman Chris Davis and
Mike Trout, who has been a finalist in each of his first two major league seasons.
The winners will be revealed next week live on the MLB Network, beginning Monday with the two rookies of the year and concluding Thursday with the MVPs.
Oakland's Bob Melvin is trying to become the first repeat winner of the AL Manager of the Year award and a three-time winner overall. Also nominated in the AL are Cleveland's Terry Francona and John Farrell of the World Series champion Red Sox, both in their first season with new ballclubs.
In the NL, Atlanta's Fredi Gonzalez, Pittsburgh's Clint Hurdle and the Dodgers' Don Mattingly will all be vying for their first awards. Managers of the year will be picked on Tuesday.