Marlins general manager Dan Jennings confirmed there is light at the end of the tunnel in Alvarez's recovery.
Last Thursday, Alvarez threw 50 pitches in an extended spring game in Jupiter, Fla.
"The fact that he's not sore" is good, Jennings said Monday. "He got through the 50 pitches the first time. Next, he will get to 75. If he feels good tomorrow, then maybe one more rehab start, and maybe big leagues."
If Alvarez does need one more rehab assignment start, it would likely be Sunday. That would line the right-hander up to be reinstated May 22 against the Orioles at Marlins Park.
Miami's Opening Day starter, Alvarez made two starts and went 0-2 with a 4.50 ERA before he experienced arm discomfort April 12 against the Rays.
The fact he could be returning before June would be a big boost to Miami's rotation.
"It's been good," Jennings said. "His progression, where he is right now, after we see tomorrow, what he feels like after that, we'll have a realistic timetable for his return."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.