Rodriguez tested positive for two anabolic steroids during his MVP season with Texas in 2003, Sports Illustrated reported on its Web site Saturday.
The New York Yankees star has long denied using performance-enhancing drugs. He declined to discuss the tests when approached by SI on Thursday at a gym in Miami.
"You'll have to talk to the union," he said.
Major League Baseball and the players' union issued statements Saturday, refusing to confirm or deny the report, citing player confidentiality.
An e-mail from The Associated Press to Rodriguez's agent, Scott Boras, was not immediately returned. The Yankees and Rangers declined comment.
The SI revelations come at a time when baseball's focus on drugs has concerned Bonds and the legal maneuvering leading to the start of his trial March 2. The government is trying to prove Bonds lied when he told a grand jury he never knowingly took performance-enhancing drugs.
A three-time AL MVP, Rodriguez has hit 553 career homers. At age 33, the All-Star third baseman is the highest-paid player in baseball and regarded by many as the most likely to break Bonds' record of 762.
Four sources told SI about his drug tests.
Rodriguez's name appears on a list of 104 players who tested positive for performance-enhancing drugs in a 2003 baseball survey, SI said. He reportedly tested positive for Primobolan and testosterone.
Baseball's drug policy prohibited the use of steroids without a valid prescription since 1991, but there were no penalties for a positive test in 2003.
The results of the testing of 1,198 players were meant to be anonymous under the agreement between the commissioner's office and the union.