The two are playing through nagging knee issues. Morrison had surgery on his right knee in December, and Stanton has dealt with pain in his left knee.
Both were in the lineup on Thursday night in the series finale against the Phillies, but they may sit a game out over the weekend.
On Friday night, Morrison likely will get a day off in the series opener with the Astros at Marlins Park. Stanton will be asked if he can go on Friday.
"There is a pretty good chance we're going to get home pretty late tonight, so there is a good chance [Morrison] probably won't play [Friday]," bench coach Joey Cora said. "We'll ask Stanton if he's available. Until they're 100 percent, it's going to be tough to get them out there five, six, seven times in a row."
In Spring Training, Stanton appeared in eight Grapefruit League games, and he had 21 at-bats. Morrison, meanwhile, had 15 at-bats in five games.
"We've got to take care of them because we're thinking about October," Cora said. "We're not thinking April. In the meantime, those two guys didn't have Spring Training. We've got to get them at-bats to get them in baseball shape."
"It's a balancing act between getting them out there playing and getting them out there healthy as much as we can. We're thinking of the whole year. We're not only thinking April. So we're going to take care of them."