Prado has been on the 10-day disabled list since May 29 with a left hamstring strain, and Cooper is on the 60-day DL with a right wrist contusion.
Of the two, Prado appears to be the closest to rejoining the club. Cooper started his rehab assignment Monday with Class A Advanced Jupiter, and after playing back-to-back games for the Hammerheads, he will head to Triple-A New Orleans on Wednesday to continue his rehab games.
"Martin has been a surprise that he's doing this well this fast," manager Don Mattingly said. "I'll say it like that. He's doing really well."
Mattingly didn't rule out Prado being back before the All-Star break. Cooper could use close to or all of the 30 days he is allotted on rehab assignment.
Prado has yet to start his rehab assignment, but he's been hitting, fielding and running.
"He's been fine," Mattingly said of the veteran third baseman's running. "Everything has been good. He's doing some kind of running progression, and he's taking ground balls."
Cooper suffered his injury in the second game of the season when he was struck by a pitch from Cubs right-hander Kyle Hendricks on March 30.
Cooper opened the season as the starting right fielder. But with rookie Brian Anderson stepped in at right field and playing a high level, Cooper will play mostly left field and first base, and occasionally in right, in his rehab games.
"It's pretty much left and first base, and a little bit of right," Mattingly said of Cooper. "He's looked comfortable in the outfield. We'll just give him enough mix to keep him comfortable in both spots."
Once Prado and Cooper are ready, the organization will have to make some decisions. With Prado out, Miguel Rojas has played mostly third base, with JT Riddle playing shortstop against right-handed pitchers.
Rojas, who opened the year at short, and utility player Yadiel Rivera have each played shortstop, third, second and first. Riddle is primarily at shortstop, but also has played second and third in the past.
Anderson, who has been among the most productive rookies in the National League, opened the year at third base. But with Prado's return expected in a few weeks, the club is keeping Anderson mostly in right field, although he occasionally goes to third base, like he did in the ninth inning Monday in Miami's 5-4 comeback win over the Giants.
"We know we'll get Martin back at a certain point," Mattingly said. "We mix and match with Miggy and JT at short, and Miggy and Yadi some at third. We know Brian can play third. He's taking enough ground balls to keep him accustomed to being in the infield. It's probably a tougher adjustment coming in [to the infield] than it is going out. He's made that adjustment really well, going to right field. But we're not abandoning third base."