The 39-year-old Griffey had narrowed his search for a new home to Seattle, where he starred from 1989-99, and the Braves, a team his father played for in the 1980s and long on Junior's wish list.
Atlanta third baseman Chipper Jones said he's talked with Griffey by phone, hoping to persuade him to sign with the Braves.
"Certainly all signs point to this being a good fit for him," Jones said after a spring training workout. "He's wanted to play here for a long time. Now he gets his opportunity. We'll see if he follows through."
There were conflicting media reports on Griffey's status, with one saying he had already chosen to play for the Braves and was merely trying to hammer out the details on a contract that would guarantee him about $2 million, with a chance to earn more through incentives.
But his agent, Brian Goldberg, told The Associated Press in a text message Tuesday afternoon that no decision had been made, and Griffey himself told mlb.com that he was going back and forth on what to do.
"We are still kicking things around with my family and have not made a decision," he said. "This is the first time in my career that I have been a free agent, and it's nerve-racking."
He added that he hoped to decide by this morning, perhaps in time to report to the Braves for their first full-squad workout.
Griffey lives in Orlando, Fla., and signaled that Atlanta had the upper hand in the negotiations because he could be closer to his family, both in spring training and during the season.
"You know how close I am to my wife and kids," he told mlb.com.
Braves manager Bobby Cox said he would be thrilled to have Griffey on a team that's trying to bounce back from its worst season since 1990. Atlanta went 72-90 and finished fourth in the NL East.
"Two years ago, he hit 30 homers," Cox pointed out.
Jones said he would love to have a guy with 611 career homers hitting behind him.
"If he wants to come here and be part of this, hit in the middle of the lineup and play a lot, it's a good spot for him," Jones said. "I would welcome him with open arms. I know that he's still Ken Griffey Jr. He's got some good baseball left in him."
ATLANTA POWER OUTAGE
Ken Griffey Jr. is past his prime, but he would help Atlanta's woeful outfield. His 2008 power numbers were more productive than any of the Braves' outfielders.
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