(CBS) The White Sox don’t currently have a time frame in mind — that they’re willing to share publicly, at least — for the arrival of 20-year-old outfield prospect Eloy Jimenez in the big leagues.

Amateur scouting director Nick Hostetler just wants fans to know that when it’s time for the White Sox to compete, Jimenez will certainly be ready.

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“This kid’s a major league hitter,” Hostetler said in an interview with Matt Spiegel and Danny Parkins on 670 The Score on Tuesday. “You can see it in his approach, the way he takes at-bats, he takes pitches, his strength. Offensively, there’s not anything he can’t do. He can move extremely quick if needed. Luckily, we don’t need it yet. But once we do, he’s going to be an integral part of this core.”

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Acquired in the Jose Quintana trade with the Cubs in mid-July, Jimenez has been on a tear since being promoted to Double-A Birmingham in mid-August, hitting .340 with three homers, six RBIs and a .960 OPS in 14 games there. It’s left the White Sox thoroughly impressed and been a continuation of a big year for Jimenez, who’s hit .308 with 19 homers, 64 RBIs and a .947 OPS in 85 games across two minor league levels.

Hostetler has been pleased with how Jimenez and other prospects in the organization have handled each challenge along the way and spoke to that idea in general terms.

“You can have all of the physical talent, all of the physical tools, if you’re not ready (mentally) or emotionally for the next step, it’s not going to work,” Hostetler said. “And some of these guys, that next step is big. When you go from (Class-A) Winston-Salem to Birmingham or Birmingham to (Triple-A) Charlotte, that’s a huge step.

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“We all make sure these guys are ready … No need to rush.”