Kimbrel completed a bullpen session Monday and could begin throwing live batting practice by the end of the week, Mark Gonzales of the Chicago Tribune reports.

Kimbrel is at the Cubs' spring training facility in Arizona as he progresses toward a return to major-league action after an extended offseason. The 31-year-old could seemingly head to Triple-A Iowa for some tune-up innings next week if all goes well during live batting practice.

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