Any suspensions for first offenders would be put on hold if the union files a grievance, a process that would put the matter in front of an arbitrator and delay possible sanctions for weeks or months. Second offenders would serve suspensions during the grievance process.
Baseball's drug agreement calls for a 50-game suspension for a first offense, 100 for a second and a lifetime ban for a third.
While most past suspensions have been for positive drug tests, the drug agreement prohibits players from using or possessing banned performance-enhancing substances and allows for discipline for "just cause."
Among the players linked to the clinic, Cabrera, Colon and San Diego catcher Yasmani Grandal already have served 50-game suspensions following positive tests for testosterone announced by MLB last year.
Most players have denied the Biogenesis link either directly or through spokesmen or lawyers.
Rodriguez admitted in 2009 that he used performance-enhancing drugs while with the Texas Rangers from 2001-03. As baseball's highest-paid player with a $28 million salary this year, he would lose $7.65 million during a 50-game ban.
Rodriguez, who turns 38 next month, has not played since hip surgery in January and is not expected to be available to the New York Yankees until after the All-Star break. The third baseman, a three-time AL MVP, has been working out since May at the team's minor league complex in Tampa, Fla.
In addition to Rodriguez, Yankees catcher Francisco Cervelli was linked to the clinic. Cervelli, currently on the DL because of a broken hand, said he consulted Biogenesis for a foot injury, but didn't receive any treatment.
"We'll let MLB handle everything and we don't really have a comment," Yankees manager Joe Girardi said after Tuesday's 4-3 win over Cleveland.
Girardi said the Yankees still planned for Rodriguez to rejoin the team after the All-Star break. As for the drug cloud that has hovered over baseball for years, Girardi said: "I think we all had hoped we'd gotten through it. But obviously, we haven't."