Kinsler, who is on the disabled list because of a right groin strain, is restricted to cardiovascular conditioning until he undergoes an MRI, scheduled for Monday in Texas.
"We'll see where I'm at, go from there," Kinsler said on Thursday afternoon. "Hopefully by then, I should be able to hit."
Until then, Kinsler can get his heart pumping but nothing more. He went on the DL on July 29.
"He hasn't done any baseball stuff yet," manager Ron Washington said. "Hopefully, we're getting close to doing that."