The newspaper, citing a high-ranking Major League Baseball official who had spoken with Selig, said the commissioner wants a decision from Giambi by Tuesday. The official was not given permission to comment publicly and spoke on condition of anonymity, the paper said.
Selig said June 6 that he wanted Giambi to meet with Mitchell within two weeks and to "cooperate fully" with the probe, which began in March 2006.
Baseball said Selig would make a decision on disciplining the New York Yankees designated hitter after Giambi "completed his activities" with Mitchell and that Giambi's level of cooperation would be taken into account by Selig.
The players' association said Giambi, currently on the disabled list with a foot injury, would make his decision after consulting with his lawyer and the union. No active players are known to have spoken with Mitchell.
MLB rules call for a 50-game suspension for a positive test for steroids or other illegal performance-enhancing drugs. Since the policy was implemented, Giambi has not tested positive. Selig could also fine Giambi, the newspaper reported.
Giambi told a federal grand jury in December 2003 that he used steroids and human growth hormone, the San Francisco Chronicle reported in December 2004. Before the start of spring training in 2005, the 2000 AL MVP made repeated general apologies at a news conference but never used the word "steroids." He told USA Today in comments published May 18: "I was wrong for doing that stuff," comments many interpreted as an admission he used steroids.
In a written statement last week, Selig said, "Any admission regarding the use of illegal performance-enhancing substances, no matter how casual, must be taken seriously."
"It is in the best interests of baseball for everyone, including players, to cooperate with Sen. Mitchell in his investigation so that Sen. Mitchell can provide me with a complete, thorough report," he said.
Baseball and its union didn't ban steroids until September 2002 and didn't institute penalties for a first offense in most cases until 2005. Michael Weiner, the union's general counsel, said no grounds exist for disciplining Giambi based on the remarks published by USA Today or Giambi's decision about whether to meet with Mitchell.