But it's unlikely that Francisco will be ready by then. The Rangers want him to make at least one or two appearances on a medical rehabilitation assignment at Double-A Frisco before they activate him again.
"This time, we're going to be a little more cautious," assistant general manager Thad Levine said.
Francisco was on the disabled list from May 7-21 with a strained right shoulder and was activated without going on a rehab assignment. This time, he'll likely pitch for Frisco on Thursday and at least one more time before the Rangers decide if he's ready to pitch in the Majors.
"It's possible he could join us in San Francisco, but it's not the plan for him to be there on the first day," Levine said.
Francisco, who has a 0.46 ERA and is 12-for-12 in save opportunities, threw both long toss and in the bullpen on Sunday without any problem.
"I feel good," Francisco said. "I think I can go, but we'll see."
Francisco will throw another bullpen session on Tuesday and possible live batting practice to hitters. A rehab assignment will be the next step. This time, the Rangers want to make sure he's completely healthy.
The Rangers had held off putting Francisco on the disabled list because they kept thinking he was a few days away from being able to pitch. But he hasn't been in a game since saving the Rangers' 4-2 victory over the Yankees on June 3. That's almost two weeks ago, and it's no longer realistic that Francisco is close to being ready to pitch in a game.
Putting him on the disabled list allows the Rangers to send him out on a medical rehabilitation assignment.
"We'd like to have something more than just live BP," Levine said.
Madrigal is joining the Rangers for the third time this season. He has a 10.13 ERA over eight relief appearances with them and a 2.53 ERA in 16 relief appearances at Triple-A Oklahoma.
T.R. Sullivan is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.