Stephenson was the 27th overall pick by the Reds in 2011 and is the organization's No. 2 prospect and was ranked Wednesday as the No. 7 right-handed pitching prospect in baseball by MLBPipeline.com. Lorenzen, the organization's No. 6 prospect, was the 38th overall selection in the first-round supplemental portion of the 2013 Draft.
Francis, a veteran of the Rockies, signed a Minor League contract Monday.
Last month, the Reds invited 10 other non-roster players to camp, including veteran pitcher Chien-Ming Wang.
Reds pitchers and catchers report to Spring Training in Goodyear, Ariz., on Feb. 14 and will hold their first workout that same day. The full squad is slated to report and work out Feb. 19.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.