The meeting was held amid a report in Wednesday's New York Daily News that said he failed an MLB-administered test for amphetamines within the past year.
Published reports said that Giambi was accompanied to his meeting at 245 Park Avenue in Manhattan by his agent, Arn Tellem, along with lawyer Brian O'Neill and Michael Weiner, a top lawyer for the MLB Players Association. Major League Baseball was represented by Rob Manfred, baseball's executive vice president for labor relations; Frank Coonelly, a senior vice president; and Howard Ganz, an outside counsel.
Citing unnamed sources, the Daily News reported that the 36-year-old slugger is subject to six additional tests for one year for failing the amphetamines test. As a first-time offender, Giambi is not subject to financial penalties or a suspension.
Major League Baseball officials are not permitted to discuss the results of testing for amphetamines, as that information is intended to remain confidential.
"I can't really talk about anything," Giambi responded Tuesday night when asked by the Daily News about the amphetamines test. Tellem also declined comment to the newspaper.
The past week has been a tumultuous one for Giambi, who implied his past use of performance-enhancing steroids to a USA Today reporter during the club's series in Chicago.
In the USA Today report, Giambi told a reporter that he was wrong for having done "that stuff" and suggested that Major League Baseball should apologize to its fans for the use of performance-enhancing drugs in the sport -- a remark that Yankees general manager Brian Cashman, among others, expressed dissatisfaction with.
During the course of the USA Today interview, Giambi said that he is "probably tested more than anybody else" -- a statement that would be backed up by the increased testing issued to Giambi due to the reported failed amphetamines test.
On the field, Giambi's 2007 season has been a trying one, as it has for many of the Yankees, who entered Wednesday's affair with the Boston Red Sox four games under .500 at 20-24. Giambi has battled a bone spur and plantar fasciitis in his left foot, which he said has made it difficult to push off while batting.
With a set of custom-made orthotic inserts having been delivered to Yankee Stadium over the weekend, Giambi slugged his sixth home run on Tuesday against Boston -- an upper-deck shot to right field -- but is batting just .268 with 19 RBIs.
"Jason's tough as nails," manager Joe Torre said. "We all know everybody is tested [for amphetamines]. We don't know any of the results. But as far as the things that are in the newspaper and talked about, when you're here a certain number of years, you get pretty much used to dealing with it and going out and doing your job."
Giambi has also fended off media reports that the Yankees may be considering the option of terminating his contract due to the steroids admission, or trading the slugger to another club. Giambi, who has a full no-trade clause and would have to approve any deal, said Tuesday that he has no intention of doing so.
"It's all news to me," Giambi said. "I have no [desire] to go anywhere. I'm a Yankee. This is all news to me. It's kind of fun to read."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.