"We just wanted to get another arm, have him available," D-backs manager Chip Hale said. "He's been throwing really well in Mobile. He's figured some things out."
Leone was 1-1 with a 4.58 ERA in 12 games for Mobile, but he also had a .242 opponents against average.
The D-backs need a starter for Thursday's game after Chase Anderson went on the disabled list on Sunday. Adding Leone to the bullpen could allow the club to avoid using long reliever Josh Collmenter out of the 'pen, which would free him up for a spot start later this week.
If not, Hale said the D-backs would likely send down a reliever should they choose to recall a starter from the Minors for Thursday.
Dorn was recalled on Sunday after Anderson went on the DL but had just one at-bat as a pinch-hitter in his stint with the club. He is batting .167 overall in 23 games with the D-backs this season.
Jake Rill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.