Maddon said Thursday he thought the 31-year-old right-hander might be ready to pitch in about three weeks.
"I would imagine in the position that's he's been in, he had some kind of a strategy of program mapped out," Maddon said. "The first thing you do is find out and then set up program. You think about a three-week window, normally it sounds right. Think about relief pitchers in spring training. Conventionally it would be like that kind of a window. But you've got to talk to the guy first and see what he's been doing."
Kimbrel, who has 333 saves and a 1.91 ERA over nine major league seasons, turned down a $17.9 million qualifying offer from Boston last November and remained a free agent. Starting this week, a team could sign him without the loss of amateur draft picks or international signing bonus pool allocation.
Chicago's bullpen has 11 blown saves this season. Brandon Morrow has not returned from offseason elbow surgery, and Pedro Strop came back Tuesday from a hamstring injury that had sidelined him since May 6. Strop and Steve Cishek have shared the closer's role.
"When you get a guy like Kimbrel, whoever was being utilized [as closer], who was in that role easily steps aside," Maddon said. "When the whole group realizes this makes us better, then everybody falls in line."