Phillies manager Rob Thomson said that Turner (hamstring) ran at a higher intensity Saturday, Corey Seidman of NBC Sports Philadelphia reports.
Turner could progress to running the bases as soon as the Phillies' series in San Francisco against the Giants which begins Monday. He will need to complete that step and also see live pitching before being cleared to begin a rehab assignment, but rehab games wouldn't seem to be too terribly far off if he continues moving in the right direction.