Kimbrel (wrist) will throw a live batting practice session Tuesday, Marc Topkin of the Tampa Bay Times reports.
Kimbrel had made only one appearance for the Rays before going down with a right wrist strain at the end of May. It's unclear whether the club will ask him to make any rehab appearances first, but Kimbrel looks to be on track for activation from the 15-day injured list when first eligible Friday.