Rienzo made his Major League debut last season and was 2-3 with a 4.82 ERA in 10 starts. He struck out 38 in 56 innings but also walked 28.
"He came up and started out pretty good but command was an issue for points when he was pitching," Ventura said. "He can work on that. I'd say he's probably on the outside with a chance to work his way into it."
Rienzo figures to be in competition with fellow right-hander Erik Johnson and left-handers Eric Surkamp and Charlie Leesman.
Chris Gabel is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.