Kimbrel (wrist) threw a bullpen session Saturday and is close to facing hitters, Marc Topkin of the Tampa Bay Times reports.
Kimbrel landed on the 15-day injured list May 31 due to a right wrist strain. However, the veteran right-hander expressed confidence Saturday that he'll be ready to be reinstated from the IL when eligible June 12. Kimbrel signed a major-league deal with the Rays on May 26, four days after being designated for assignment by the Mets.