"I did take a banned substance. And for that, I am very sorry and deeply regretful," he told ESPN.
Players besides Braun and Rodriguez that might face discipline include Everth Cabrera, Melky Cabrera, Francisco Cervelli, Bartolo Colon, Nelson Cruz, Gio Gonzalez, Yasmani Grandal, Fernando Martinez, Jesus Montero, Jordan Norberto, Jhonny Peralta and minor-leaguer Cesar Puello.
The ESPN report says Gonzalez could be exonerated because the Washington Nationals pitcher purchased substances from Bosch that are not banned by MLB.
Melky Cabrera, Colon and Grandal were each suspended last season for 50 games after they tested positive for elevated testosterone levels.
"I don't know anything about [the report]," Cabrera told USA Today. "This is the first I hear of it. If they suspend me again, I think that would be a harsh punishment because I already served my sentence. But it's up to them."
ESPN also says the MLB could look into New York Yankees' second baseman Robinson Cano for possible connections to Bosch's clinic. The spokeswoman for Cano's foundation, Sonia Cruz, was listed in Biogenesis documents and MLB officials are looking into whether she might have been a conduit for Cano.
The Major League Baseball Players Association issued a statement Wednesday, saying it has been working with MLB throughout the course of its investigation into Biogenesis.
"The Players Association has every interest in both defending the rights of players and in defending the integrity of our joint program. We trust that the Commissioner's Office shares these interests," MLBPA Executive Director Michael Weiner said in a release.
Dr. Gary Wadler, an associate professor of medicine at Hofstra University Medical School and a former official with the World Anti-Doping Association, called the possible suspensions "distressing" and "not terribly surprising."
"Compared to where we are when I testified before Congress in the 2005 baseball hearings, we are eons ahead," Walder told U.S. News. "Baseball has come a long, long way, but it is not a perfect system."
Major League Baseball did not return requests for comment on the ESPN report.