The Marlins, off on Thursday, will be home facing the Nationals at Marlins Park beginning on Friday.
"We feel like he's probably ready right now," Marlins manager Don Mattingly said on Tuesday.
Asked if Jackson could be reinstated when the club returns home, Mattingly responded: "Yes."
Miami's bullpen has been heavily used, especially during this road trip, which included a doubleheader on Saturday at Washington.
When he rejoins the club, Jackson will be a long relief option.
In his first rehab appearance, Jackson threw about 50 pitches in three innings. He gave up three runs on five hits with a walk and three strikeouts.
While Jackson is on the brink of being reinstated, lefty reliever Mike Dunn remains on pace to return either in late May or early June. Dunn, on the DL all season with a left forearm strain, added a slider to his last bullpen session after his first one featured all fastballs.
"I know once he starts getting to those games, the 'pens are coming closer together," Mattingly said.
Before being reinstated, Dunn will pitch in at least four rehab-assignment games. His last hurdle will be throwing in back-to-back games.
"We're getting him closer," Mattingly said. "We'll try to get him back-to-back somewhere, to makes sure he is able to bounce back."