The sides are trying to reach as many agreements as possible that would avoid grievance hearings, and talks could push back an announcement until Friday.
The meeting between MLB and the union on Tuesday, first reported by the New York Daily News, signalled the final stretch of talks. MLB hopes to announce the penalties for all players involved at the same time, both people said, speaking on condition of anonymity because no announcements were authorized.
Three-time MVP Alex Rodriguez of the New York Yankees stands to receive the longest suspension. While 50 games is the standard for a first offence, the stiffer penalties for some players are tied to other alleged violations, including not being truthful to MLB investigators.
Three 2013 All-Stars could face bans: Texas outfielder Nelson Cruz, San Diego shortstop Everth Cabrera and Detroit shortstop Jhonny Peralta. In a sign Peralta's suspension might be imminent, the Tigers acquired shortstop Jose Iglesias from Boston on Tuesday night as part of a three-way trade with the Chicago White Sox.
"The frank reality is that I do not know what is going to happen with Jhonny, but with this move, we now feel well protected if there is a long suspension," Tigers general manager David Dombrowski said.
Another 2013 All-Star, Oakland pitcher Bartolo Colon, was suspended last year following a positive testosterone test, as were Toronto outfielder Melky Cabrera and San Diego catcher Yasmani Grandal. They won't receive additional discipline for that violation, the two people said.
Yankees catcher Francisco Cervelli and Seattle catcher Jesus Montero also have been linked in media reports to Biogenesis, a closed Florida anti-aging clinic that was accused by Miami New Times in January of distributing banned performing-enhancing drugs.
Melky Cabrera was the 2012 All-Star game MVP while with San Francisco and Colon won the 2005 AL Cy Young Award with the Los Angeles Angels.
Players who don't reach agreements can ask the players' association to file grievances, which would lead to hearings before arbitrator Fredric Horowitz. Discipline for first offenders under the drug agreement usually is not announced until after the penalty is upheld, but there is an exception when the conduct leading to the discipline already has been made public.
In addition, MLB may try to suspend Rodriguez under its collective bargaining agreement instead of its drug rules, which would lead to the suspension starting before the appeal.
Milwaukee outfielder Ryan Braun was the first player to reach an agreement with MLB. The 2011 NL MVP accepted a season-ending 65-game suspension last week. Braun tested positive for elevated testosterone in October 2011 but a 50-game suspension was overturned the following February by an arbitrator who ruled Braun's urine sample was handled improperly.
Rodriguez faces the harshest penalty. The Yankees expected him to be accused of recruiting other athletes for the clinic, attempting to obstruct MLB's investigation, and not being truthful with MLB in the past when he discussed his relationship with Dr. Anthony Galea, who pleaded guilty two years ago to a federal charge of bringing unapproved drugs into the United States from Canada.
"A-Rod was my teammate in New York. I'm glad he was my teammate," retired pitcher Roger Clemens said Tuesday in Boston, where he was at Fenway Park to mark the 25th anniversary of manager Joe Morgan's team that won the 1988 AL East title.
"I did things to make him feel comfortable. I did that for all of my teammates," Clemens said. "I think I was a pretty solid teammate."
The seven-time Cy Young Award winner was acquitted last year of federal charges he lied to Congress when he said he didn't take steroids or human growth hormone.
Clemens would not give his thoughts on MLB's Biogenesis investigation.
"I've got my own feelings on particular people in MLB, you know, how they approached my situation," he said. "I don't know about it, and I don't care about it, to tell you the truth."
AP freelance writer Ken Powtak in Boston contributed to this report.