"Hopefully Alex will be back shortly thereafter," Yankees general manager Brian Cashman said.
Rodriguez didn't stop to talk with reporters after his workout Wednesday at the team's minor league complex in Tampa, Fla.
At first, MLB and the union thought talks on the Biogenesis probe could be completed by Friday, but negotiations to avoid grievances are likely to push back announcements until at least Saturday or Sunday.
Others accused in media reports of receiving performance-enhancing drugs from Biogenesis include a trio of 2013 All-Stars: Texas outfielder Nelson Cruz, San Diego shortstop Everth Cabrera and Detroit shortstop Jhonny Peralta.
Most of the players face 50-game bans as first offenders. Both sides felt an urgency to complete the process because by the middle of next week, teams will have fewer than 50 games left. And that would force players to complete suspensions during the playoffs or at the start of next season.
Detroit general manager Dave Dombrowski protected against a possible suspension of Peralta by acquiring slick-fielding infielder Jose Iglesias from Boston in a three-team trade Tuesday night.
"If it were a 15-day thing, like a typical injury, I think we could have comfortably dealt with it with the players we already have," Dombrowski said Wednesday. "But when you start to talk about 50 days and a possible playoff run, we feel better going ahead with Jose."
While MLB told the union which players it intends to suspend, it hasn't issued formal notices of discipline. Because of that, the countdown hasn't started under baseball's Joint Drug Agreement, which says the suspensions are effective on the third business day after the notice is issued.
The sides also haven't decided whether suspensions for first-time offenders who challenge the penalty can be announced before an arbitration decision.