NEW YORK — David Ortiz hopes to begin taking batting practice in the cage either Monday or Tuesday, but the hulking DH is feeling frustration over the slow progression of his rehab effort.

Ortiz has been sidelined since June 1 with a left wrist injury and remains on the disabled list.

“It takes me a while to get wound up and hit,” said Ortiz, who has been hitting flips (soft tosses) for the last week. “I still feel the pain. It’s not what I felt in there before, but I still feel it. I’ve got to work through it. I’m not pain-free yet.”

Recalling his initial swings last week off the soft tosses, Ortiz chuckled and said, “Everything was (hit) right into the ground. Then I started to get the ball into the air. I still have some weakness in there. It’s a funky kind of injury.”

Ortiz said he’s accepted the fact that he’s going to have to fight through some discomfort when he returns to the lineup. Asked when that might be, Ortiz indicated the Sox had hoped he might be ready to go out on a minor-league rehab assignment “around the All-Star break.”

However, such a timetable means that Ortiz would have only a week of hitting in the cage and live batting practice before beginning his rehab stint.

And that assumes that there will be no further setbacks or further down time that might be necessary if the pain continues or intensifies as the workload grows.