Going into Tuesday's game at Ohio State, Trimble leads the Terps with a career-high 17.1 points, 3.8 rebounds and 3.4 assists a game.
Maryland (19-2, 7-1) is tied with Wisconsin for first place in the Big Ten.
The Terps, who moved up from No. 22 to No. 17 in the Associated Press Top 25 on Monday, have won six straight games and are 4-0 on the road in the Big Ten.
Trimble will be trying to duplicate the feat of former Maryland All-American Greivis Vasquez, who won the Cousy Award in 2010.
He is the only point guard in the Big Ten to make the list of finalists. The list will be cut to five next month.
The others named Monday were:
Nigel Williams-Goss, Gonzaga
Monte Morris, Iowa St.
Frank Mason, Kansas
De'Aaron Fox, Kentucky
Joel Berry II, North Carolina
Dennis Smith, North Carolina State
Lonzo Ball, UCLA
Jalen Brunson, Villanova
Markelle Fultz, Washington