Hill is scheduled to hit again in an intrasquad game Wednesday before taking Thursday off.
"If he doesn't have any discomfort that he can't deal with, then he's going to proceed forward with it," D-backs manager Kirk Gibson said.
• Closer J.J. Putz, who is on the disabled list with a strained right elbow, threw his second bullpen session Tuesday and is expected to face hitters -- including Hill -- for the first time Friday.
"J.J. threw very well and felt good," Gibson said.
• The D-backs' one-run win Monday was their 15th of the year, most in the Majors. The A's and Padres are tied for second with 13.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.