According to the report, which was posted Saturday morning on SI.com, sources told the publication that Rodriguez was on a list of 104 players who tested positive that year, when Major League Baseball conducted tests to see if mandatory random drug testing was needed.
In 2003, there were no penalties for a positive result.
Rodriguez, reached at a Miami gym for comment by Sports Illustrated, said, "You'll have to talk to the union."
Asked if there were an explanation for the positive test result, Rodriguez told SI: "I'm not saying anything."
Sources confirmed to ESPN's T.J. Quinn that Rodriguez was aware he tested positive for steroids in 2003, but it was not clear when he learned of the result.
A-Rod, By The Numbers
Alex Rodriguez belted a career-high 57 home runs in 2002, a year before he won his first of three MVP awards and reportedly tested positive for testosterone and an anabolic steroid as baseball conducted survey testing.
2002 2003 2004
BA .300 .298 .286
HR 57 47 36
RBI 142 118 106
SLG .623 .600 .512
Major League Baseball, in an agreement with the MLBPA, wanted to see if random drug testing should be implemented starting in 2004.
More than 5 percent of players in the majors tested positive in the '03 survey, and mandatory testing was implemented -- including provisions for penalties -- in 2004.
Even if Major League Baseball were to confirm that Rodriguez was one of the players to test positive in 2003, he would not be subject to any sort of discipline based on that testing.
However, if information emerges about positive tests from 2004 on, circumstances could change. There have been players connected with HGH purchases from 2004 and forward, for example, who have been subject to discipline by the commissioner's office.
Scott Boras, Rodriguez's agent, did not immediately return calls from ESPN.com seeking comment.
Both the Yankees and the Rangers told ESPN they would not comment.
Michael Weiner, general counsel for the players' union, declined to comment, and said he did not know if the union would have any comment Saturday.
Major League Baseball plans to release a statement regarding SI's report later Saturday.
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