Mattingly said Puig took swings on Saturday against Dodgers reliever Brandon League, who is on the 60-day disabled list with a right shoulder injury he suffered in Spring Training.
"He hit off of League today," Mattingly said. "He ran curves today. I think Yasiel is moving forward."
Puig has been on the disabled list since April 26 with a left hamstring injury. His previous rehab stint with Class A Advanced Rancho Cucamonga was cut short when the injury began bothering him again. Puig was hitting .279 in 11 games before going on the DL.