Berkman, diagnosed with left biceps tendinitis, responded favorably after hitting off a tee and hopes to take some swings in a game soon, perhaps by Tuesday.
"I'm going to try to DH [Tuesday]," Berkman said. "That's what I'd like to do, if they'll let me."
Later in the day, manager Cecil Cooper said he will not use the DH on Tuesday. Cooper indicated he might give Berkman another day and put him in the lineup Wednesday.
Berkman swung from both the left and right sides off the tee, and he thinks if he can keep both hands on the bat when he swings right-handed, he should be OK. He originally hurt the shoulder taking a high number of right-handed swings in the cage the other day.
"If I make a conscious effort to hold onto the bat, I can do it," he said.
Berkman couldn't lift his arm higher than a 90 degree angle when he first injured his shoulder, but by Monday, he had improved, slightly. Still, when he tried to raise his arm above his head, he had to stop, admitting, "That still hurts."
"But," he added, "If you're alive, you're going to experience pain."
Asked to place a percentage on his odds to appear in another exhibition game this spring, Berkman answered, "100 percent."
"It certainly feels better today than it did [Sunday]," Berkman said. "And I think that's always a a positive."
In other camp news, the back end of the Astros' bullpen -- Doug Brocail, LaTroy Hawkins and Jose Valverde -- were all scheduled to throw in a Minor League game at Osceola County Stadium on Monday.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.