Griffey did not do any running on Thursday, but he was expected to test his leg with a running session before Friday's game.
Third baseman Edwin Encarnacion also sat out another game while he mended his mildly sprained left ankle.
Encarnacion rested on Thursday and took a break from running and baseball activities. Mann said that the swelling was reduced and that Encarnacion would take batting practice and ground balls on Friday.
"It feels great," Encarnacion reported. "[It] feels a lot better than yesterday. I can work better now."
Rich Aurilia started at third base in place of Encarnacion.
With the depth of his bench particularly strong this season, Narron didn't feel the need to rush injured players back to the lineup, especially in the infield.
"If Edwin's down, you got Rich Aurilia, [Scott] Hatteberg [and] Rich are interchangeable, Freelie anywhere on the infield except short," said Narron. "We've got some veteran guys there [on the bench], which is outstanding."
Despite not starting, both Griffey and Encarnacion were available to pinch-hit.
LaRue feeling fine: With his single in the eighth inning on Wednesday, catcher Jason LaRue broke an 0-for-29 slump.
Despite hearing all the whispers about his early season struggles, LaRue insisted that nothing was wrong.
"I've actually felt great," said LaRue. "I'm seeing the ball well. For whatever reason, I've always started off slow, and in this game, you can't panic."
"I really can't explain, last year or this year, why he's gotten off to slow starts," Narron said. "We're just fortunate that David Ross has stepped in and played real well."
With Bronson Arroyo on the mound on Thursday, Ross was back behind the plate. He is in the midst of a 10-game hitting streak, batting 13-for-28 (.464), with two homers and 10 RBIs.
Despite LaRue's struggles, Narron remained confident that LaRue will find his hitting stroke soon.
"I think at some point, he'll get hot and get some big hits for us," said Narron.
"I feel comfortable, [and I] have felt comfortable," LaRue said. "We'll just see what happens here, try to keep it going."
Bullpen sessions: Starting pitcher Paul Wilson is scheduled to throw a 30- to 40-pitch session in the bullpen on Friday. It will be Wilson's first appearance on a mound since he suffered a setback in a Minor League rehabilitation assignment in early May.
On Saturday, reliever Matt Belisle will also throw a 30- to 40-pitch bullpen session. Belisle has been on the disabled list since May 30 with a strained lower back.
Redlegs Run results: The Reds hosted their fifth annual "Reds Run for Home," a charitable 5K run to benefit the Reds Community Fund, on Sunday.
More than 2,000 runners turned out to participate in the race, which finished on the field at Great American Ball Park. More than $54,000 was generated for the fund, whose proceeds will be used for youth outreach baseball programs throughout Cincinnati.
In addition, the top five male and female finishers were honored on Thursday before the game, and the winners threw out the first pitch.
Coming up: Elizardo Ramirez (2-4, 3.95) will get the start for the Reds opposite Greg Maddux (6-5, 4.77) of the Cubs in the second game of a four-game series against Chicago on Friday night at 7:10 ET.