The three former managers and nine other candidates will be presented to the Hall of Fame's 16-member Expansion Era Veterans Committee when they vote Dec. 9.
Torre led the New York Yankees to four world championships in a five-year span from 1996-2000, also winning six American League pennants with the team. His 2,326 wins are the fifth-most in MLB history.
La Russa notched the third-most managerial wins in baseball history with 2,728. He won three World Series, including one with Oakland (1989) and two with St. Louis (2006 and 2011).
Cox, meanwhile, has the fourth-most MLB wins 2,504 wins over 29 seasons with the Atlanta Braves. He guided them to five World Series appearances and one win in 1995, as well as to 14 consecutive division titles from 1991-2005.
Also on the ballot will be former Yankees owner George Steinbrenner and manager Billy Martin as well as ex-players Dave Concepcion, Steve Garvey, Tommy John, Dave Parker, Dan Quisenberry and Ted Simmons and former Players Association executive director Marvin Miller.