CHICAGO — Carlos Lagrange may still be a long shot to impact the Yankees this season — assuming he is not traded in the next week — but his progress from a shoulder injury has at least kept the door open.

The top pitching prospect, who was diagnosed with a capsular sprain of the right shoulder July 3, has resumed throwing on flat ground after about a four-week shutdown — two weeks shorter than the club originally estimated for him.

The 23-year-old Lagrange, who was in the midst of a transition from starter to reliever in hopes of helping the Yankees bullpen in the second half, still has a ways to go to even potentially make himself an option. But the earlier-than-expected return to throwing at least keeps the possibility in play for the time being.

“We’ll see,” manager Aaron Boone said Tuesday before the Yankees’ 3-2 win over the White Sox when asked if he expected Lagrange to become a consideration at some point this season. “He has started throwing again, so you never know for sure. But we’ll just listen to his arm and body and hopefully, as he starts his throwing progression, things go well and he puts himself in position to be in the conversation. But impossible to know right now.”

On Tuesday, Lagrange posted video to social media of himself throwing, though Boone said he actually started throwing “a handful of days ago.” Lagrange last pitched at Triple-A on June 28, with the shoulder diagnosis coming a few days later.

Yankees prospect Carlos Lagrange delivers a pitch during a spring training outing earlier this season. Charles Wenzelberg / New York Post

The Yankees are still expected to add a high-leverage reliever or two before Monday’s trade deadline, but if Lagrange is not used in a package to make that happen, his rehab process will be worth monitoring to see if he can become a wild card late in the season.

One of those bullpen targets the Yankees are believed to be pursuing is Padres stud closer Mason Miller.

It remains to be seen whether the Padres will actually make him available, but Boone was asked for his thoughts on the hard-throwing righty.

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“Feels like a speculative question cloaked in an opinion on a player,” he said with a grin. “Look, obviously he’s one of the game’s great closers and has been now for a few years. Tremendous stuff. I don’t even know if he’ll be moved or not. He’s probably as good as is out there right now in that role.”

The Yankees signed veteran catcher Christian Bethancourt to a minor league deal Tuesday and added him to the roster at Triple-A Scranton/Wilkes-Barre for depth.

The 34-year-old, who has played 427 career big league games, had been at Triple-A for the Cubs this season, batting .262 with a .775 OPS in 59 games.