LOS ANGELES -- The Dodgers don't have written criteria for retiring uniform numbers. But with one notable exception, each of the franchise's 10 retired numbers was worn by a player or manager who spent the majority of his career with the Dodgers and was inducted into the Baseball Hall of Fame.

The one exception is longtime Dodger Jim Gilliam, who was the club's first-base coach when he died suddenly at age 49 just before the start of the 1978 World Series. His number was immediately retired.

Players such as Fernando Valenzuela and Steve Garvey, award winners but not Hall of Famers, have not had their numbers retired, although nobody has worn Valenzuela's No. 34 since he left the club in 1991.

• Dodgers' retired numbers

With those parameters, the candidates for the next Dodgers uniform number most likely to be retired are Clayton Kershaw (22), Maury Wills (30), Garvey (6), Valenzuela (34), Gil Hodges (14) and Don Newcombe (36).

The unknown on Kershaw isn’t if, but when. The three-time National League Cy Young Award winner and 2014 NL MVP won’t be eligible for the Baseball Writers’ Association of America Hall of Fame ballot until he has been retired for five seasons, and his current contract expires after the 2021 season. Even if he retires then at age 33, the earliest he could be a Hall of Famer is the 2027 induction.

By then, Wills will have had two more cracks at Hall of Fame election by the Golden Days Committee, which is charged with reviewing players active from 1950-69 that the BBWAA voters overlooked. Hodges, who died at age 47 while managing the Mets, also falls into the Golden Days playing window and many feel he is one of the most glaring omissions for the Hall. But in its most recent vote, the committee showed much more support for Wills.

Garvey is another player who has been snubbed by the writers and various veterans committees, despite appearing in 10 All-Star Games, which pretty much defines the word "fame." Newcombe, who died last year, was a four-time All-Star and the first player to win a Rookie of the Year, Cy Young and MVP award (since accomplished by Justin Verlander), but he lost two seasons in his prime serving in the military during the Korean War.

The wild card in the Dodgers equation is whether the club would break from custom and retire the number of Valenzuela, now a Spanish-language broadcaster with the club and one of its most popular players ever.

Although shoulder problems derailed his greatness, Valenzuela made the game accessible to the vast Mexican-American market with Fernandomania. He won the NL Cy Young and Rookie of the Year awards in 1981 but was dropped off the BBWAA ballot after two years when he failed to receive the necessary 5 percent of the vote.

Here are the Dodgers’ retired uniform numbers: (1) Pee Wee Reese, (2) Tommy Lasorda, (4) Duke Snider, (19) Gilliam, (20) Don Sutton, (24) Walt Alston, (32) Sandy Koufax, (39) Roy Campanella, (42) Jackie Robinson and (53) Don Drysdale.