Collins, 26, missed the entire 2015 season after undergoing Tommy John surgery during spring training.
Before his surgery, Collins had made 228 relief appearances in four MLB seasons with the Royals. In that time, Collins accumulated a 3.54 ERA with 220 strikeouts and 121 walks in 211 innings.
Collins turned in his best season in 2012, when he recorded a 3.36 ERA with 93 strikeouts in 69 2/3 innings.
The Royals have seven remaining arbitration-eligible players ahead of Wednesday’s tender date: pitchers Louis Coleman, Danny Duffy and Greg Holland, catcher Drew Butera, infielder Mike Moustakas and outfielders Lorenzo Cain and Jarrod Dyson.