The award, in its twelfth year, is named after the former Holy Cross and Boston Celtics star. Maryland's Greivis Vasquez won it in 2010.
The list will be narrowed to five players by early March, and the award will to be presented April 10 on ESPN2's national award show.
Trimble, the Terps' star freshman, is averaging 16.1 points, 3.6 rebounds and 3.1 assists per game.
Earlier this week, his teammate Jake Layman was listed among the candidates for the inaugural Karl Malone Power Forward of the Year Award.
Here are the 17 candidates for the Cousy Award:
T.J. McConnell, Arizona
Tyrone Wallace, California
Kyle Collinsworth, Brigham Young
Ryan Boatright, Connecticut
Tyus Jones, Duke
Kevin Pangos, Gonzaga
Keifer Sykes, Wisconsin-Green Bay
Yogi Ferrell, Indiana
Monte Morris, Iowa State
Terry Rozier, Louisville
Melo Trimble, Maryland
Marcus Paige, North Carolina
Kris Dunn, Providence
Delon Wright, Utah
Nigel Williams-Goss, Washington
Juwan Staten, West Virginia
Fred VanVleet, Wichita State