Gardner, 29, entered play on Saturday batting .288 with seven home runs, 29 RBIs and 11 stolen bases in 79 games, bouncing back from a season in which he was limited to 16 games because of an injured right elbow.
Gardner has hit safely in 26 of 32 games since May 24, batting .331 over that stretch. He had a .347 on-base percentage and .450 slugging percentage entering Saturday.
The only Yankees outfielder to rank near the top of any balloting update was Ichiro Suzuki, who clocked in at 15th at each checkpoint. Robinson Cano has led AL second basemen at each update.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.