CHICAGO -- The Cubs are one day closer to circling a date on the calendar for the arrival of Craig Kimbrel. Following Kimbrel’s scheduled Minor League appearance for Triple-A Iowa on Tuesday, Chicago's decision-makers will convene with the closer to determine his next step, and whether that will be joining the Cubs.

"Tuesday is an important checkpoint for us to see how he's feeling," Cubs president of baseball operations Theo Epstein said on Monday. "We'll get together with him and make a call after that game and see what direction we go."

Depending on Kimbrel's feedback, Epstein said, there is a chance that the right-hander could be called to Chicago before the conclusion of the current homestand or early on the next road trip. The Cubs are hosting the Braves through Thursday before heading to Cincinnati for a three-game weekend series against the Reds.

Kimbrel, who signed a three-year contract worth $43 million on June 7, threw in consecutive games for Iowa on Friday and Saturday before entering a two-day down period. The closer worked 19 pitches on Friday and then another 14 on Saturday, giving him three total Minor League outings.

Epstein said the most important part of the situation is listening to Kimbrel's thoughts on his schedule.

"He's such a pro and, obviously, a veteran," Epstein said. "He knows himself better than anybody else. Getting his input is important. We're getting close to the point where we'll have established enough of a foundation where there's an opportunity to take the next step provided he feels good with everything."

When Kimbrel does arrive, Cubs manager Joe Maddon said, the closer will be eased into the bullpen mix. It will be treated similar to how relievers are used in April, following Spring Training and an offseason. With Kimbrel coming back from a longer "offseason" than typical, Maddon added, he would be limited to three-out appearances for the next couple months.

"As he gets here, he'll be slotted in really carefully," Maddon said. "And then, as we get there to the latter part of September, if it's necessary, that's when I think you look for the four outs possibly -- sometimes, I hope not, five. But, I also believe that this bullpen, with the experience that we've gotten to this point, should hopefully avoid that by being able to absorb the eighth inning well.”

Injury updates

• Epstein noted that right-hander Kyle Hendricks (10-day injured list, right shoulder inflammation) threw 15 pitches in a light mound session on Monday. Hendricks might be cleared to throw a full bullpen session later this week, and Epstein said that a return "around the All-Star break" is a possibility, barring any setbacks.

• Righty Carl Edwards Jr. (10-day IL, left thoracic strain) has built up to 120 feet in long-toss and is closing in on a mound session, per Epstein. The Cubs will want Edwards to complete a handful of bullpen workouts before building a game progression, which will likely include a rehab assignment

• Reliever Brandon Morrow (60-day IL, right elbow surgery) has completed two mound workouts in Arizona and is scheduled to throw another one in the next couple days. Said Epstein: We'll keep it going slow with him, but it's certainly good news that he's up off the mound and feeling really good."

• Epstein indicated that shortstop prospect Nico Hoerner (broken left wrist) is working through baseball activities in Arizona and might be cleared to begin rehab games there by the end of the week. Hoerner is the Cubs' No. 1 prospect, per MLB Pipeline.

Worth noting

• Triple-A Iowa infielder Robel Garcia was released by the Indians in March 2014 and he was out of affiliated baseball until the Cubs signed him to a Minor League contract in October. Last year, the switch-hitter suited up for UnipolSai Bologna in the Italian Baseball League. In 65 games between Double-A and Triple-A this year, Garcia has hit .294 with 19 homers and a .981 OPS in 65 games, while mostly splitting time between second and third.

The 26-year-old Garcia, who hit his 13th homer at Triple-A on Monday, has the Cubs' attention.

"You've got to pay attention to guys performing at the level that he is and offers the different skills that he has," Epstein said. "Anyone at the Triple-A level is certainly on the radar screen. Yeah, we've spent a lot of time watching him, evaluating him, talking about him. We're looking forward to the next phases of his development."

• With Kimbrel coming soon, and pitchers such as Hendricks and Edwards on the comeback trail, the Cubs could have a roster crunch in their future.

"It's a wonderful problem," Maddon said. "If you can have a problem of too much pitching, my God, I'll take that every day and twice on Sundays. I'll take that. We have tried to attempt to figure this out right now and, weirdly, I've talked about this before, baseball has its own way of figuring things out."