"I contacted some of them, and some have contacted us," Goldberg said Friday. "We're still talking and there is no deadline for him to sign. He's confident that he'll play somewhere next season."
Goldberg said six of the organizations are in the American League, but would not name any of them. Nor would he disclose which three National League teams have shown interest in the 39-year-old Griffey.
The Mariners' offices at Safeco Field were closed for the Thanksgiving holiday, so team officials could not be reached for comment.
Interest in Griffey could go in either direction on Monday, the last day for clubs to offer salary arbitration to their free agents. Although the White Sox, who acquired Griffey from the Reds last August, decided not to pick up the option year of his contract for $16.5 million, they still could offer the Type B free agent salary arbitration and receive a supplemental Draft choice if he signs with another organization.
Griffey would have until Dec. 7 to accept or reject the salary arbitration offer.
One potential issue -- the left knee that bothered him most of last season and led to postseason surgery -- apparently is not an issue at all.
"I talk to Junior two or three times a week, and he's feeling great," said Dr. Tim Kremcheck, the Reds physician who performed arthroscopic surgery on Griffey's knee in October. "He's running, lost some weight -- about 12 pounds -- and has been able to do more aerobic workouts than before.
"As good as he feels right now, he's ready to play another couple of years, and that's exciting."
The knee, which might have been injured in late April when Griffey banged it against a trunk inside the Reds' clubhouse, began giving him trouble in May. But instead of having surgery at that time and being sidelined for six to eight weeks, he decided to delay the procedure until after the season.
"Junior played through the pain until there was fluid buildup," Goldberg said. "He tried to play through it and didn't want to shut it down."
The knee was drained of fluid three times, twice while he was with the Reds, and Kremcheck said that was the primary reason Griffey's production slid from 30 home runs and 93 RBIs in 2007 to 18 home runs and 71 RBIs in '08.
Goldberg said Griffey, who ranks fifth on the all-time home run list with 611, is eager to play for at least one more season.
"Kenny realizes that he probably would be a middle-ground guy when it comes to salary," he said. "He also understands that a contract could include some incentives, but I don't think he'll price himself out of a job. He's never been about being the highest paid."
Goldberg said Griffey would be receptive to a one-year contract offer from "the right team in the right place," but wouldn't be any more specific than that.
The Mariners would seem to be one of the teams at least interested in discussing a deal with their former first-round Draft choice and eventual 10-time All-Star center fielder.
They ranked near the bottom of the league in run production last season and need more firepower, preferably from the left side, especially if free-agent left fielder Raul Ibanez leaves as expected.
Futhermore, Griffey has said several times that he would like to finish his career where it began, and a lot of Mariners fans would like to see a reunion.
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.