"I anticipate him being ready to go," Marlins manager Mike Redmond said.
Recovering from last September's surgery on his right knee, Morrison opened the season on the DL. Because of so much lost time, he has taken the full 20 days allotted to position players on rehab assignment.
Morrison has played in 15 rehab games total, with nine at Double-A Jacksonville. He has had 55 at-bats.
When Morrison returns, he will take over at first base.
The knee hasn't given him any trouble. A main reason he stayed the full 20 days is to get as many at-bats as possible after he missed some much time dating back to last year.
While Morrison could be back in a couple of days, there is uncertainty regarding right fielder Giancarlo Stanton.
Stanton is on a rehab assignment with Class A Jupiter, but because of rainouts, he hasn't played since Wednesday.
Stanton, on the DL with a strained right hamstring, has appeared in two games and has six at-bats.
Nathan Eovaldi, out with right shoulder inflammation, is scheduled to make a rehab assignment start for Jacksonville on Sunday. If all goes well, the right-hander could be joining the Marlins at the end of next week.
"I think it's good news that guys are coming, and hopefully coming soon," Redmond said. "That will definitely help us out."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.