CHICAGO -- The White Sox appear to have a major addition coming for their American League Central-leading roster around the Trade Deadline, and they won’t have to give up anything or anyone to bring him aboard.

That addition, of course, is Eloy Jiménez, the Silver Slugger-winning left fielder who has hit 45 home runs and driven in 120 over 730 career plate appearances. The team announced Thursday the beginning of a Minor League injury rehab assignment for Jiménez, who had surgery to repair a ruptured left pectoral tendon two days before the start of the regular season. That assignment begins Friday with High-A Winston-Salem, putting Jiménez well ahead of schedule for a return.

Even without Jiménez, the White Sox carried a 51-35 record and eight-game lead over the Indians into Thursday’s off-day. They are a very good team in a less-than-stellar division, and the club will only improve once Jiménez’s powerful presence is in Chicago.

“They have not given me a timeline,” said Jiménez during a Thursday Zoom session, when asked if there was a target date for his comeback. “But I think I can be there at the end of this month. That’s my thought, but I don’t know. They don’t tell me when I’m going to be there.

“I feel better than Spring Training. I feel like 100%, 110% -- let’s say 200%. So I feel pretty normal. I feel like I can go and do my swing, finish with one hand, two hands, whatever.”

Jiménez suffered his injury chasing a Sean Murphy fly ball and making an ill-advised leaping attempt to snag the home run in a March 24 Cactus League game against Oakland. Jiménez’s left arm hung on the wall and stretched out after the jump.

Andrew Vaughn, who was being looked at as the Opening Day designated hitter and a backup to José Abreu at first base, moved to left field for three games at the end of Cactus League action and has handled the position more than capably. Adam Engel returned from the injured list prior to Wednesday’s game, serving as an important outfield pickup for the White Sox, who also are getting outfield contributions from Brian Goodwin, Billy Hamilton, Leury García and the young bat of Gavin Sheets.

White Sox manager Tony La Russa pointed to using Jiménez as the DH a lot over the season’s final two months in a pregame media session Wednesday. But it’s never been a position Jiménez desires, and despite his vast excitement to return, it still isn’t.

“Well, I have to keep working hard and if they need me playing, I’ll do whatever,” said Jiménez of a potential DH role. “But I still don’t like DH, so keep that in mind.”

Credit was given by Jiménez to his teammates for their support and keeping his spirits up over the last few months, even though it has been tough at points for Jiménez to watch his friends playing, because he wants to be there. He has been working of late in Arizona with center fielder Luis Robert, who suffered a complete tear of his right hip flexor while trying to beat out an infield single in the first inning of a May 2 loss to Cleveland. They have pushed each other and could be back in the same big league lineup in the not-too-distant future.

“We helped each other. We tried to compete,” said Jiménez of Robert. “Tried to do our best every single day and we put the effort in to be the best, so that’s why we are going to be back sooner than later. We motivate each other.”

This non-game action certainly hasn’t dampened Jiménez’s always sunny outlook, as he began Thursday’s Zoom with a boisterous “Good morning, everyone!” to all the reporters. It certainly was a good morning for the White Sox and Jiménez with the latest development.