Online fan voting opened Wednesday and runs through July 15 at ESPN.com.
Joining Curry and James in the best male athlete category are Green Bay quarterback Aaron Rodgers and Houston Texans defensive end JJ Watt.
Besides Williams, UFC fighter Ronda Rousey, Connecticut basketball player Breanna Stewart and Olympic skier Lindsey Vonn are nominees for female athlete. Rousey earned another nod for best fighter, along with Floyd Mayweather Jr. Vonn was nominated for best comeback athlete.
The awards, hosted by Joel McHale, will air July 15 from Los Angeles on ABC.
Triple Crown winner American Pharoah is nominated for best championship performance, along with three humans: San Francisco Giants pitcher Madison Bumgarner, Florida softball pitcher Lauren Haeger and James. Victor Espinoza, who rode American Pharoah, is nominated for best jockey.
Masters and newly crowned U.S. Open winner Jordan Spieth and Little League World Series star Mo'ne Davis are among the nominees for best breakthrough athlete.
The nominees for best coach or manager are: Geno Auriemma of UConn women's basketball, Bill Belichick of the New England Patriots, Steve Kerr of Golden State, Mike Krzyzewski of Duke, and Urban Meyer of Ohio State football.
Patriots quarterback Tom Brady earned a nod for best NFL player, along with Pittsburgh wide receiver Antonio Brown, Philadelphia Eagles running back DeMarco Murray, Rodgers and Watt.
Williams earned a second nomination as best female tennis player.