The suspensions, which do not include New York Yankees third baseman Alex Rodriguez, were not confirmed by MLB or the players and their teams.
Foxsports reported the 12 had accepted 50-game bans.
They included a number of players who had already been named by U.S. media but the report did not list Rodriguez, who has been the focus of MLB's long investigation into links between players and a Florida clinic accused of supplying performance enhancing drugs.
Several U.S. media organisations have said an announcement on the investigation was expected sometime on Monday.
By accepting 50-game suspensions now, players would be sidelined for around eight weeks but would be back in time to rejoin their teams for any postseason playoffs.
Before Monday, only one player had been suspended over the Biogenesis investigation.
Milwaukee Brewers slugger Ryan Braun, the National League's Most Valuable Player just two years ago, accepted a 65-game bad, ruling him out for the rest of this season.