"That's what the plan is right now," Dunn said.
The Marlins are the only team in the Majors without a lefty in their bullpen, but that will change when Dunn is ready.
Dunn threw 27 pitches on Saturday, with 10 warmups and 17 against a hitter. The hitter actually was one of the club's two hitting coaches, Frank Menechino, who saw pitches from the right and left sides of the plate.
"It was scheduled to be a bullpen, but I asked for hitters," Dunn said. "It was going to be 25-30 pitches. I did 10 warmups."
The next step for Dunn is to go on rehab assignment on Tuesday when he will pitch for Class A Advanced Jupiter. If that goes without a glitch, Dunn will then pitch back-to-back days on Thursday and Friday for Jupiter.
As a final tuneup, he will throw in an extended spring game on May 30.
"That's just to be ready to go," Dunn said.
There is a chance the schedule could be accelerated and Dunn rejoins the team sooner than early June. But the team has been extremely careful in his recovery, and he last pitched in a game on March 24 in Spring Training.
Dunn notes he sees the "light at the end of the tunnel."
If he is reinstated on either June 1 or 2, it will be when the Marlins face the Pirates at Marlins Park.
Joe Frisaro has covered the Marlins for MLB.com since 2002. 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.