Thames went on the 15-day disabled list on June 13 with a strained right hamstring and is slightly ahead of schedule. He's hitting .244 with two home runs and 10 RBIs in 33 games this season.
Additionally, right-hander Alfredo Aceves is continuing to rehab from a strained lower back in Tampa, Fla., and played long toss again on Tuesday. That is not insignificant -- Aceves felt pain while throwing off flat ground in Tampa on May 25, a setback from an injury that sent him to the 15-day DL on May 12.
"He's definitely lasted down there longer than the last time," Yankees manager Joe Girardi said.