"I think the easy thing to say is Gleyber comes into Major League camp and competes, but starts at Triple-A because that's the safest route," Cashman said. "But I'm not denying anybody a chance to make the club and push their way into the mix."
With Todd Frazier now a free agent, Cashman sees the 33-year-old Headley as an option to slide back in at third base, saying that it will be his to defend from a group that includes Torres, Tyler Wade and Miguel Andujar, the Yanks' No. 5 prospect.
"Whether it's Gleyber Torres, whether it's Andujar, whether it's [outfielder] Clint Frazier, those guys are all serving notice on the more established players of, 'Don't sleep on us, because we're trying to take what you've got,'" Cashman said.
The centerpiece of the July 2016 Aroldis Chapman trade with the Cubs, Torres is capable of playing second base, third base and shortstop. There were those last spring who believed Torres could make the jump to the big leagues, even though he had not played a single game above Class A.
When Yankees vice president of baseball operations Tim Naehring passed through Double-A Trenton on a scouting trip early in the season, he reported to Cashman that Torres appeared ready to be promoted to Triple-A Scranton/Wilkes-Barre at any point.
Torres hit .273/.367/.496 in 32 games at Double-A before getting the bump up to Triple-A, where he posted a .309/.406/.457 slash line in 23 games before tearing the ulnar collateral ligament in his left elbow during a June 19 game in Buffalo, N.Y.
While Torres is believed to be close to 100 percent and even asked to play winter ball, the Yankees told him that they would prefer to finish off the last stages of his rehab in a controlled environment.
"I'd say it's nice to have the young guys pushing up," Cashman said. "It's nice to have the older guys hear the footsteps. We'll have our fresh eyes on the new blood trying to make a name for themselves. Sometimes it does happen."
Bryan Hoch has covered the Yankees for MLB.com since 2007. Follow him on Twitter @bryanhoch and on Facebook. This story was not subject to the approval of Major League Baseball or its clubs.