Michael Kopech and Eloy Jimenez … coming soon to the White Sox? Don’t bet on it

When a reporter asked when he would be able to see top prospects Michael Kopech and Eloy Jimenez, White Sox general manager Rick Hahn could not resist cracking wise.

“Well, they are available at Charlotte and Birmingham,” he said.

Indeed, Chicago-area Sox fans won’t see either, and perhaps for a little while, unless they go on a trip or subscribe to MiLB.TV.

“As thrilling as it would be to have one or both up here tonight,” Hahn said, “perhaps to show some level of advancement in this rebuild, what happens here will have nothing to do with when these players arrive. It’s going to be based strictly upon their own development and when they are ready for the challenges presented by the big-league level.”

Jimenez has cooled off a bit at Double-A Birmingham, going 5-for-22 since June 3, but still leads the Southern League with a .576 slugging percentage. Jimenez will stop at Triple-A Charlotte before joining the big club, Hahn said.

As for Kopech, it’s a bit more complicated.

He has had dominant starts, poor starts and everything in between. His last outing was a mixed bag — two earned runs over six innings, 10 strikeouts, five walks.

“He’s certainly getting closer,” Hahn said.

Lucas Giolito (7.08 ERA entering Monday) has been permitted to work out his issues in Chicago. Why not Kopech?

“There’s no doubt these guys could come here and survive right now, especially if we wanted to drop (Kopech) in the ’pen and use him for one or two innings every so often,” Hahn said. “That’s not what we are trying to do.

“In Michael’s instance, we’re trying to develop a front-end starter. The difference between players who may not be having success up here is that they already have answered some of those questions at the minor-league level. They checked the boxes.

“There may come a point where you may have them go back for another finishing touch, take a half-step back (in the minors) to take two steps forward. But how any individual is doing in Chicago has zero impact on Michael Kopech’s developmental plan or when Michael Kopech gets here. He’s in control of that.”

Feeling it: Avisail Garcia’s strained right hamstring cost him a week of April, all of May and a nice chunk of June. But finally Garcia is ready to embark on a rehab assignment. He is slated to spend seven to 10 days in Charlotte, beginning Tuesday.

Said Hahn: “It’s more getting into baseball shape at this point than anything physical with the hamstring.”

Ready to roll: Right-hander Alec Hansen, the sixth-ranked prospect in the Sox’s system, according to MLB.com, will make his season debut this weekend for Birmingham. Hansen, a second-round pick in the 2016 draft, has been sidelined by a forearm injury since spring training. Last season he struck out a combined 191 batters among three levels.

tgreenstein@chicagotribune.com

Twitter @TeddyGreenstein

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