He retired in 2010 fourth behind La Russa in career wins with a record of 2,504-2,001. Cigar-chomping and fiercely loyal to his players, Cox was ejected a major league record 159 times.
Two of his pitchers during the team's remarkable stretch during the '90s, 300-game winners Greg Maddux and Tom Glavine, head the newcomers on this year's players' ballot. Results of voting by the Baseball Writers' Association of American is scheduled for Jan. 8.
"It would be quite an honor to go in with those two guys," Cox said. "I just hope Glav and Mad Dog can be on the stage with me. That would be the final finishing touch, going in with those two."
Marvin Miller, the pioneering head of the players' association from 1966 to 1981, was rejected for admission to the Hall for the sixth time he appeared on a committee ballot. He fell one vote short of induction in 2010 and received no more than six votes this year.
"Words cannot adequately describe the level of disappointment and disbelief I felt when learning that once again the Hall of Fame has chosen to ignore Marvin Miller and his unparalleled contributions to the growth and prosperity of Major League Baseball," players' association head Tony Clark said in a statement. "Over the past 50 years, no individual has come close to matching Marvin's impact on the sport. ... Despite the election results, Marvin's legacy remains intact and will only grow stronger, while the credibility of the Hall of Fame continues to suffer."
Former union chief Don Fehr also lamented Miller's nonelection, calling him the most important person to baseball in the second half of the 20th century, with Jackie Robinson being the most important in the first half.
"His positive impact on baseball simply can't be overestimated," Fehr said in a news release. "Marvin should have been elected to the Hall many years ago. It is a sad and sorry state of affairs that he has not been, and continues to reflect poorly on the very organization that has as its purpose recognizing and celebrating baseball's best."
This year's committee included Hall of Famers Rod Carew, Carlton Fisk, Whitey Herzog, Tom Lasorda, Paul Molitor, Joe Morgan, Phil Niekro and Frank Robinson; Blue Jays president Paul Beeston; retired club executive Andy MacPhail; Phillies president Dave Montgomery; White Sox chairman Jerry Reinsdorf; Steve Hirdt of the Elias Sports Bureau; Bruce Jenkins of the San Francisco Chronicle; BBWAA secretary-treasurer Jack O'Connell; and retired Fort Worth Star-Telegram reporter Jim Reeves.
This year's ballot, chosen by a BBWAA-appointed historical overview committee, covers baseball's expansion era. Players, managers, umpires and executives whose most significant impact was from 1973 on were considered as part of a three-year cycle. The golden era (1947 to 1972) will be voted on in 2014 and the pre-integration era (1871 to 1946) will be judged in 2015.
Torre had an unusual experience when he learned of his election from Hall chairman Jane Forbes Clark.
"I was always trying to be like blasé about this, saying that it's something I never obsessed about, because I had no control over it," he said. "But when the phone call comes and -- I hung up on Jane Clark the first time she called this morning, not meaning to, but I didn't have my glasses on -- it hits you like a sledgehammer."
Information from The Associated Press was used in this report.