The 39-year-old star's contract is for one year and believed to be worth $2 million in base salary, plus incentives.
Earlier in the day, a person with knowledge of the negotiations told the Associated Press that an apparent agreement with the Atlanta Braves had fallen through.
Atlanta appeared to be Griffey's choice Tuesday for the same reason he left Seattle for the Cincinnati Reds in 2000: geography. The Braves' spring training camp is about a 20-minute drive from the Griffey family home in Orlando, Fla., and Atlanta is about an hour away by plane.
The Mariners have a job as designated hitter and perhaps in left field waiting for Griffey, who is fifth on baseball's career home run list with 611. The Braves were offering a possible platoon in the outfield.
Griffey made his first Opening Day start with the Mariners as a 19-year-old in 1989. He stayed 10 more years before the trade to the Reds. He has been hampered by injuries since and had arthroscopic knee surgery after the 2008 season, the last half of which he spent with the Chicago White Sox.
The players association was contacted by the commissioner's office to set up an interview involving Rodriguez and the sport's investigations department, union general counsel Michael Weiner said.
Weiner said the interview will be nondisciplinary in nature but declined to comment further.
At a news conference Tuesday, Rodriguez said he had been injected with a banned substance from 2001 to 2003 while with Texas. He said the substance, which he called "boli," was obtained by a cousin in the Dominican Republic whom he wouldn't identify.
A baseball official told the Associated Press that MLB would like to learn the identity of the cousin and the source of the "boli" that he obtained and injected into Rodriguez.
Rodriguez was the last of 60-plus Yankees to take the field for the team's first full-squad workout yesterday in Tampa, Fla.
Some of the 1,200 or so fans gathered at Steinbrenner Field cheered when they saw No. 13. Not a single boo or insult was heard. Yankees fans are as forgiving as Rodriguez's teammates.
"We're here to support him through it," Yankees captain Derek Jeter said. "... It's our jobs to try to help him be as comfortable as he can on the field and try to move past this."
Red Sox: : Owner John Henry renewed his call for a salary cap after an offseason in which the Yankees added three free agents for $423.5 million.
Or, as Red Sox president Larry Lucchino said, "the Yankees have spent like the U.S. Congress."
The Red Sox owners are troubled by the wide disparity in team payrolls that they say limits competitive balance in baseball - even though Boston had the second-highest payroll at the end of last season.
Nationals: : A top baseball prospect from the Dominican Republic who received a $1.4 million signing bonus from Washington lied about his age and name in what team president Stan Kasten is calling "an elaborate scheme."
In July 2006, the Nationals held a news conference to announce they signed Esmailyn "Smiley" Gonzalez, a 16-year-old shortstop. He led the Rookie-level Gulf Coast League with a .343 average in 2008.
But while the Nationals have been listing his date of birth as Sept. 21, 1989 - which would make him 19 - Kasten said yesterday that a Major League Baseball investigation determined Gonzalez is actually Carlos David Alvarez Lugo, born in November 1985 - meaning he is really 23.
More Nationals: : Outfielder Josh Willingham agreed to a $2.95 million contract for 2009.