The award will be announced Monday at 8 p.m. on the MLB Network.
Price, 27, won 20 games this season for the Rays. He amassed a 2.56 ERA, which led the American League, and struck out 205 batters in 211 innings pitched. His WHIP checked in at 1.10.
Price is a three-time All-Star. He finished second in the American League Cy Young voting in 2010, the year Price won the Players Choice Award for the American League outstanding pitcher award.
Sale, 23, won 17 games for the White Sox this season. He had a 3.05 ERA and struck out 192 in 192 innings in his first season as a starter.
Weaver also won 20 games this season. He has a 2.81 ERA and a league-leading 1.02 WHIP.