Judge and Goldschmidt are both finalists for the Most Valuable Player honors that will be presented next week by the Baseball Writers' Association of America.
Now a free agent, Judge hit 62 home runs last season with the New York Yankees, topping the American League record of 61 set by Roger Maris in 1961.
Judge also led the majors in slugging percentage (.686), on-base percentage (.425), OPS (1.111) and runs (133), and his 131 RBIs tied Pete Alonso of the Mets for most in the big leagues. Judge batted .311, second in the AL, and was in contention for a Triple Crown until the final days of the season.
Goldschmidt led the NL in slugging percentage (.578) and on-base average (.404) while hitting .317 with 35 home runs and 115 RBIs. The Cardinals first baseman also won the Hank Aaron Award in 2013 with Arizona.
Every team nominates candidates for the Aaron awards. A group of MLB.com writers choose the eight finalists in each league, and fan votes are added to the picks by a panel of Hall of Fame players.
The awards are sanctioned by Major League Baseball and named for the Hall of Fame Braves outfielder.