Beckham has swung a weighted bat and took some hacks in the cages Sunday at Camelback Ranch. Those swings were not at full force needed for game action.
"I don't have an answer for that yet," said White Sox general manager Rick Hahn of Beckham and a possible trip to the disabled list. "He's not really doing baseball activities. Days are getting a little short. We'll have to see how he progresses."
"It's tricky," White Sox manager Robin Ventura said. "We have to wait and make sure he's ok, doesn't go out and hurt himself again, and then you lose him for 15 more days. Just being very careful with him."
White Sox reliever Matt Lindstrom suffered a similar left oblique strain a few days before he was scheduled to make his Cactus League debut on Feb. 28. Lindstrom suffered one setback along the way and didn't end up pitching in a game until this past Friday, with a follow-up inning Sunday against the Rockies.
Options do exist if Beckham starts the season on the disabled list.
With Jeff Keppinger also probably opening on the DL because of a shoulder impingement, Marcus Semien would be the starting second baseman and either Leury Garcia or Alex Liddi moves into the utility role.
"We have some options," Hahn said. "There's no need to rush Gordon back for March 31 if it doesn't physically make sense."
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.