In one of the final hurdles, the 36-year-old ran from first to third base and from second base to home plate.
"That's where I put more stress on the knee," Griffey said. "This is probably the best I've felt running. I'm trying to push through it. "
Manager Jerry Narron and head trainer Mark Mann supervised Griffey's workout, which took place on the field at Great American Ball Park several hours before the Reds played the Nationals.
"Today by far, was his best day," Mann said. "He looked like he ran rather comfortably."
"To me, it didn't look like he was holding back," Narron said. "It looks like he's getting pretty close."
Besides running, Griffey also shagged fly balls and took extended batting practice. He hit several balls over the fence in all directions, including one impressive long ball to right field as he broke his bat.
Griffey reported there was some lingering soreness in the knee, which he hyperextended before a game at Wrigley Field nearly a month ago. He was later diagnosed with a strained biceps tendon. An MRI exam taken last week showed that some inflammation still remained.
Eligible for activation from the DL since April 28, Griffey has seen his probable return date pushed back a few times. He described one of the issues that he endured in recent weeks.
"It's one of those things," Griffey said. "Pitchers have dead arms for a while and I had a dead leg. It didn't get over the hump and now it's starting to. I think that's a good sign for me to get back and we'll just see what happens [Wednesday]."
Griffey, who is batting .258 with two homers and seven RBIs in eight games said he didn't need to be fully recovered to come back. He also said the call giving him the green light wasn't solely his to make. Narron, general manager Wayne Krivsky and team medical director Dr. Tim Kremchek will all be involved.
"I just need to feel comfortable going out there day in and day out," Griffey said. "I've done this a few times, a lot more times than I would like to have. But it doesn't have to be 100 percent."