If he emerges from the bullpen sessions feeling fine, he'll join a Minor League affiliate for a rehab start, manager Bud Black said. Kennedy will throw between 75 and 90 pitches.
"Ian is feeling good, and we're encouraged by his progress," Black said.
Kennedy only pitched 2 1/3 innings his last time out, in last Thursday's home opener against the Giants. He strained the hamstring at the end of the second inning and tried to pitch the third, but soon felt it would be smart to get out of the game and get treatment.
Odrisamer Despaigne filled in that day, retiring all 14 hitters he faced. Then on Tuesday, making his first start for Kennedy, Despaigne allowed one run in seven innings. Despaigne's next start will come on Monday in Denver against the Rockies.
Kennedy, at this point, needs to show the team his hamstring is healthy and that he has enough endurance and stamina to work deep in a game. He pitched six innings in a game the final week of Spring Training, then three innings in an exhibition game against Mexico City on April 4.
Is it possible Kennedy might need a second Minor League game to build his stamina, thus providing an opportunity for Despaigne to get a third start in his place?
"It's possible," Black said. "He's got to build his pitch-count when he starts. Then we will evaluate him after that [Monday] game."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.