The newspaper reported that two unidentified people briefed on the matter said at least one player linked to now-closed Biogenesis of America purchased documents from a former clinic employee in order to destroy them, and that other players made efforts to buy potentially incriminating documents.
In January, the Miami New Times, an alternative weekly newspaper, reported that New York Yankees slugger Alex Rodriguez was among the big leaguers listed in Biogenesis of America's records.
New Times said it obtained records detailing purchases by Rodriguez, 2012 All-Star game MVP Melky Cabrera, 2005 AL Cy Young Award winner Bartolo Colon and 2011 AL championship series MVP Nelson Cruz.
Other baseball players the newspaper said appeared in the records include Gio Gonzalez and Yasmani Grandal. Later, Yahoo Sports reported that 2011 NL MVP Ryan Braun's name also appeared in the records.
The players have denied they obtained banned drugs from the clinic that operated out of an office park in Coral Gables, Fla.
Baseball Commissioner Bud Selig has declined to comment on Biogenesis, other than to say it is the subject of a "very thorough investigation" by MLB.
The Times said the payments by the commissioner's office did not exceed more than "several thousand dollars."
MLB officials decided to take the unusual step of paying for the documents because, with no subpoena power, its investigators would likely have no access to the material if it wound up in the players' hands, The Times reported.
Last month, Major League Baseball sued Biogenesis, and its operators, accusing them of scheming to provide banned performance-enhancing drugs to players in violation of their contracts.
The lawsuit in Miami-Dade Circuit Court seeks unspecified damages from Biogenesis and its operator, Anthony Bosch. Several other Bosch associates are named in the lawsuit.
Among the banned drugs supplied, the lawsuit said, are testosterone, human growth hormone and human chorionic gonadotropin.
Baseball officials also unsuccessfully lobbied New Times editors to share the documents that formed the basis of their story.