In 13 games out of the Arizona bullpen this season, Burgos had 25 strikeouts and led Major League relievers with a 16.46 strikeouts-per-nine-innings ratio.
Reed is 2-2 with three saves and a 5.92 ERA in 25 relief appearances with the D-backs this year.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.