Rookie Eloy Jimenez returned to the White Sox’ lineup Sunday as the designated hitter. For now, anyway, the Sox don’t see that as his future home.

After being activated from the injured list (bruised ulnar nerve in right elbow), Jimenez was the DH in the Sox’ 11-1 loss to the Twins. And if Jimenez was unfamiliar with how to stay mentally sharp as a DH, he couldn’t be blamed for it. Sunday was only his second time serving as a DH in the majors.

He thought taking swings in the cage might help, but he wasn’t sure.

‘‘I think so, but I don’t know because it’s hard to know or pay attention to the game as a DH,’’ Jimenez said. ‘‘It’s hard to be focused on the game when you DH. That’s why I don’t like being a DH.’’

The Sox could have sent Jimenez out for a rehab assignment, but they chose to reinsert him into the lineup. If he had gone somewhere in the system, he still would have been a DH for a while as he went through a throwing program. So the Sox figured they rather would have him swing against big-league pitchers.

‘‘In either case, it’s DH there or DH for us here,’’ manager Rick Renteria said. ‘‘I’d rather have him DH for us here and get his bat back in the lineup.’’

There are few questions about Jimenez’s bat. He has shown the mouthwatering power that made him one of the best prospects in baseball and has learned how to manage the strike zone. He went 0-for-3 in his first game back, but a bad strike call by plate umpire Angel Hernandez in the sixth inning cost him a walk that would have brought in a run.

Jimenez’s fielding, however, has been an issue. He has landed on the IL twice after incidents in the outfield, and his jumps and judgment have been works in progress.

But Renteria wasn’t ready to say Jimenez is on track to becoming a DH. Renteria complimented his work ethic and how he has done all the tasks the Sox have asked and said he ‘‘sincerely has improved out there a lot.’’

Before games, it’s common to see Jimenez working with coach Daryl Boston on the finer points of playing in the field. And, at 22, Jimenez still has time to mature and grow with his glove, though his 6-4, 240-pound frame might limit him.

‘‘He’s too young for me to view him as a DH, to be honest,’’ said Renteria, who expected Jimenez to be back in the outfield in a few days. ‘‘And I think he’s shown so much improvement in the outfield that it would be, I think, derelict on my part and on our part as an organization to limit the ability for him to play on both sides of the baseball.’’

That would help the Sox, both now and in the future. Their roster has more than enough players who could DH, and their farm system also has pieces (Andrew Vaughn, Zack Collins, Gavin Sheets) that would fit better with Jimenez in the outfield.

‘‘So we want to see if we can maximize his ability to do everything he can as a major-league baseball player,’’ Renteria said. ‘‘And then time will tell us. If [DH] ends up ultimately being his lot . . . that becomes his lot. But I think right now we’re going to continue to use him on both sides of the baseball, for sure.’’