PHOENIX — The same day Aaron Boone announced DJ LeMahieu had been diagnosed with a non-displaced fracture in his right foot, the veteran infielder hit in the cage and continued his throwing program back in Tampa.

LeMahieu’s progress has continued in the days since, albeit in small steps, as he hit on the field Tuesday and took ground balls hit right to him on Monday at the club’s player development complex.

Boone indicated that the bigger challenge for LeMahieu would be moving side-to-side defensively.

“The last six-seven days, he’s moved in a good direction after kind of slowing down, even shut down for a couple days,” Boone said Tuesday before the Yankees’ 7-0 loss to the Diamondbacks, their first loss of the season. “We’re gonna listen to the pain and listen to the foot and he’ll heal as we go.”

The Yankees have insisted that the follow-up MRI exam revealing LeMahieu had the fracture did not change much from when he was just believed to have a significant bone bruise.

Boone was asked what would represent a significant step forward for LeMahieu in his rehab.

“I think when he gets out and he’s taking ground balls and not in pain doing it or not pushing through doing it,” Boone said. “And also moving well. … It’s about — especially with him and the things he’s been through from the lower half and the foot and the toe the last couple years — making sure he’s not playing through any kind of issue that could lead to something else.”

Gerrit Cole (elbow) is getting closer to starting a throwing program, but Boone did not have a date for when that would happen.

The reigning AL Cy Young winner was shut down from throwing for three to four weeks because of nerve inflammation and edema.

“I know he’s moving in that direction,” Boone said. “Everything seems to be going well so far.”

Oswald Peraza is about to start throwing again, ahead of schedule.

The infielder was originally scheduled to be shut down from throwing for six to eight weeks when he was diagnosed with a shoulder strain that the Yankees made public on March 9.

But Peraza is now set to begin a throwing program on Wednesday, which will mark four weeks since he last picked up a baseball.

Peraza has been hitting recently, but now he will add throwing to his rehab menu as he works towards getting back into game action.

Once Peraza is at full health, it’s possible he will just be optioned to Triple-A Scranton/Wilkes-Barre.

The 23-year-old had been fighting for a bench job in camp before getting hurt, but the Yankees have since traded for utilityman Jon Berti and Oswaldo Cabrera is off to a hot start.

The Yankees traded reliever Nick Ramirez to the Dodgers in exchange for cash considerations after designating him for assignment on Saturday.

The Yankees signed ex-Mets reliever Phil Bickford to a minor league contract Tuesday.

The 28-year-old righty had been designated for assignment by the Mets when they signed J.D. Martinez and then was released last week.

Bickford will report to Triple-A Scranton/Wilkes-Barre